Statistics

Problem 201

A survey asked students to rate their stress level from 0 (not stressed) to 10 (very stressed). Find the most common stress rating.

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Problem 202

Find the five-number summary and interquartile range for the given temperatures in $51, 54, 56, 58, 61, 61, 69, 72, 80, 81, 84$ Fahrenheit.

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Problem 203

Find the most frequently occurring value in the data set: $20, 31, 46, 31, 49, 31, 49$ .

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Problem 204

Determine if the statement "When finding the \mean, it is necessary to arrange the data items in order" is true or false. Provide the correct answer.

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Problem 205

A sample of $n=25$ produces $t=2.062$ . Researcher can reject null hypothesis with $\alpha=.05$ but not $\alpha=.01$ using two-tailed test.

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Problem 206

A magazine asked 1000 adults to identify their favorite pie. $14 \pm 3 \%$ chose chocolate pie. Which confidence interval is wider: $99 \%$ or $80 \%$ ? C. A $99 \%$ confidence interval must be wider than an $80 \%$ confidence interval in order to be more confident that it captures the true value of the population proportion.

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Problem 207

Find the probability a student without an A is female given the gender and grade data for the class.
$P(\text{Female} | \text{No A}) = \frac{P(\text{No A} \cap \text{Female})}{P(\text{No A})}$

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Problem 208

Probability that a student who did not complete homework passed a test, given data table of students who passed/failed test and completed/did not complete homework.

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Problem 209

Find the mean of the corrected list of elapsed times: $2.16, 2.88, 2.96, 2.09, 2.64, 2.36, 2.22$ .

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Problem 210

Find total variation for predicted data $(0,8), (1,5), (2,2)$ from line of best fit $y' = 8 - 3x$ . Provide actual observed data points to calculate total variation.

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Problem 211

Find the 5 number summary for the data: $93, 42, 9, 12, 86, 10, 43, 53, 89, 49, 55$ .

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Problem 212

Find the regression with the weakest linear relationship between $\mathrm{x}$ and $\mathrm{y}$ given $y=a x+b$ with $a$ and $b$ values and correlation coefficient $r$ .

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Problem 213

Find the SAT score that corresponds to the 26th percentile, given that SAT scores are normally distributed with a mean of 1090 and a standard deviation of 197.
$\text{SAT score} = 1090 + 197 \times z$ , where $z$ is the $z$ -score corresponding to the 26th percentile.

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Problem 214

Find the residual value for the coordinate (4,9) given the line of best fit $y=1.18x+5.4$ . Options: $0.86$ , $-0.86$ , $1.12$ , $-1.12$

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Problem 215

Compute the mean, median, and mode of repair costs for 4 crashes of the same car model at 5 mph. The repair costs are $429,$ 448, $486, and$ 222. A. The mean cost of repair is $\$ 396.25$ . (Round to the nearest cent as needed.)

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Problem 216

Find the probability that a randomly chosen 10-year-old in the US has height between $39.9$ and $46.4$ inches, given heights are normally distributed with mean $55.7$ inches and standard deviation $9$ inches. Round final answer to 3 decimal places.

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Problem 217

Around what percentage of adults in the USA have stage 2 high blood pressure ( $\text{SBP} \geq 160$ ) given that SBP is normally distributed with $\mu=122$ and $\sigma=16$ ? Round to two decimal places.

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Problem 218

Estimate 51 marbles in a jar, actual is 42. Find the percent error, rounded to the nearest tenth.

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Problem 219

Calculate the sample variance for the set of numbers: $10, 90, 91, 85, 57$ . Round the result to 2 decimal places.

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Problem 220

Find the percentage of data to the left of the z-score $z=1.05$ .

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Problem 221

Find the five-number summary and interquartile range for the distances (in miles) to the nearest airport for 11 families: $8, 13, 19, 19, 21, 23, 28, 28, 31, 37, 42$ .

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Problem 222

What is the unemployment rate if the job separation rate is $0.05$ and the job finding rate is $0.35$ ?

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Problem 223

Calculate the sample standard deviation of ages in a dataset of 23, 62, 22, 67. The closest approximation is $2 \sqrt{10}$ .

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Problem 224

Evaluate time series model for quarterly raincoat sales data (2010-2015) in London. Determine if statements about $Y = T + S + E$ model are true or false.

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Problem 225

Find the median weight of a sample of 13 male 11th graders with weights $152, 165, 140, 150, 175, 142, 172, 171, 156, 158, 168, 146, 160$ pounds.

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Problem 226

Find the range of the sound loudness estimates (in decibels) with a mean of $70$ : $68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68$ .

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Problem 227

Find the probability that Victoria's next bowling score, which is normally distributed with $\mu=130$ and $\sigma=11$ , falls between 123 and 130. Round the answer to the nearest whole percent.

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Problem 228

Add missing values to incomplete box plot using data set: $81, 83, 83, 83, 84, 84, 84, 84, 85, 86, 87, 88$ .

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Problem 229

Find the range of the caterpillar cocoon days: $8, 12, 5, 9, 21, 18, 9, 7$ .

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Problem 230

Find the range of pregnancy lengths that covers the middle 95% of pregnancies in a village, given a normal distribution with $\mu = 200$ days and $\sigma = 15$ days.

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Problem 231

Analyze the given stem-and-leaf plot to find the mean, median, standard deviation, and range of the data, rounding answers to one decimal place.
a. Mean: $\frac{\sum x}{n}$ b. Median: The middle value when the data is ordered c. Standard Deviation: $\sqrt{\frac{\sum (x - \mu)^2}{n}}$ d. Range 50: The difference between the 50th percentile and the 50th percentile

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Problem 232

Find the $x$ -value that separates the top 12% of a normal distribution with $\mu=52.1, \sigma=7.5$ from the rest of the data.

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Problem 233

Chemical engineer must report the average volume of a pollutant produced by plants. Data: Platte $2.772$ L, Macon $48.58$ L, South Fork $2.36$ L. What average volume should be reported with correct significant digits?

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Problem 234

Find the correlation coefficient $r$ between $\boldsymbol{X}$ and $\boldsymbol{y}$ given $\sum(x-\bar{x})(y-\bar{y})=11$ , $\sigma_x=3.62$ , $\sigma_y=3.23$ , and $n=16$ .

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Problem 235

Which measure of central tendency is most affected by the extreme value in the given half marathon pace data?
$\{6.7, 7.1, 7.5, 7.6, 3.3, 7.4, 7.2, 7.4, 7.1, 7.4, 6.8, 6.9, 7.3\}$

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Problem 236

Find the 43rd and 53rd percentiles of the ages of 29 Academy Award winning best actors, given in ascending order: $24, 27, 27, 30, 30, 36, 37, 37, 37, 39, 42, 45, 46, 47, 48, 49, 50, 51, 51, 56, 61, 63, 64, 69, 70, 71, 77, 78, 78$ .

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Problem 237

Identify the levels of measurement: $\{$ Nominal Data, Ratio, Quantitative Data, Ordinal Data $\}$

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Problem 238

Determine if the underlined value, $59\%$ of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

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Problem 239

Babies with low birth weight (< 2500 g) may have health issues. Mean birth weight is 3496 g, but 2646 g for babies born 1 month early. Find standardized score (z-score) for 2500 g birth weight for: a) all births, b) 1 month early births. Determine which group 2500 g is more common.
a. $z=-2.17$ b. $z=-0.32$ c. B. A birth weight of 2500 g is more common for all births in the country.

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Problem 240

Rewrite the problem statement: Find the frequency distribution and construct a histogram for the hottest recorded temperatures (in °F) across 16 North American cities.
$92.5-96.5$ : $\square$ $96.5-100.5$ : $\square$ $100.5-104.5$ : $\square$ $104.5-108.5$ : $\square$ $108.5-112.5$ : $\square$

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Problem 241

Find the 98th percentile of a standard normal distribution with mean 0 and standard deviation 1.

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Problem 242

Calculate the range, variance, and standard deviation for the given samples. a. $34, 47, 45, 40, 48$ , b. $100, 3, 9160, 16207$ , c. $100, 35, 40, 6040, 447$ . a. The range is $\square$ .

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Problem 243

Compare the z-scores of a 45-year-old Best Actor and a 37-year-old Best Supporting Actor with $\mu_{BA}=44.0$ , $\sigma_{BA}=7.2$ , $\mu_{BSA}=54.0$ , and $\sigma_{BSA}=16$ .
Best Actor: $z=\frac{45-44.0}{7.2} = 0.14$ Best Supporting Actor: $z=\frac{37-54.0}{16} = -1.06$

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Problem 244

Classify variables as quantitative or categorical: (a) customer satisfaction (very/somewhat satisfied/dissatisfied), (b) weight (in lbs) needed to break bridge cable, (c) cell phone service provider.

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Problem 245

Find the mode of the sample scores $[4, 14, 56, 0.8, 14, 56, 14]$ .

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Problem 246

Calculate the standard deviation of the distances (in miles) traveled to work by 5 employees: $10, 3, 14, 34, 9$ . Round the answer to two decimal places.

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Problem 247

Find the total number of registered doctors if $33.6\%$ were female and there were 48,200 female registered doctors.

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Problem 248

A manufacturer claims the mean breaking strength of new cables is greater than 1775 lbs. Test this claim using a one-tailed test with $\alpha=0.05$ . The sample mean is 1790 lbs and the population standard deviation is 55 lbs.
(a) $H_0: \mu \leq 1775$ lbs, $H_1: \mu > 1775$ lbs (b) Use a z-test (c) Test statistic $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} = 1.818$ (d) $p$ -value $= 0.035$ (e) Yes, we can support the claim that the mean breaking strength is greater than 1775 lbs.

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Problem 249

Given normal calorie burn data with $\mu=310$ and $\sigma=7$ , find probabilities of: (a) >320 calories, (b) <302 calories, (c) 298-330 calories. The probability of (b) is $12.70\%$ , and the probability of (c) is $\square$ .

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Problem 250

Determine the most accurate and precise measurements of signal speed in a nerve fiber, given a later reliable measurement of $16.0 \mathrm{~m} / \mathrm{s}$ and four teams' earlier measurements.

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Problem 251

Find the average of the numbers $49, 78, 64, 61, 69, 29, 70, 24, 25, 40, 33, 20, 35, 34$ .

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Problem 252

Approximate the mean gas mileage (in miles per gallon) from a frequency distribution of 23 cars. Round the mean to one decimal place.
$25-30: 9, 31-36: 10, 37-42: 1, 43-48: 3$

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Problem 253

Find the missing value $x$ in the set $\{4, 16, 14, x, 10\}$ if the mean is 12.

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Problem 254

What is the probability that a randomly selected high school athlete plays either football (15%) or basketball (27%), given 6% play both sports?

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Problem 255

A manufacturer's item lengths are normally distributed with $\mu = 14.2$ inches and $\sigma = 2.3$ inches. Find the probability that the mean length of 35 randomly chosen items exceeds 13.6 inches. (Round to 4 decimal places)

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Problem 256

Determine the standard deviation of the number of people with a $6\%$ genetic mutation in a random sample of 600 individuals. Round to 3 decimal places.

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Problem 257

Find the mean, median, and mode(s) of the data set $54, 44, 38, 40, 49, 43, 52, 45, 31, 35$ . Round the mean and median to one decimal place if necessary.

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Problem 258

Calculate the standard deviation of the marks of 9 students: $71, 58, 89, 93, 91, 53, 56, 86, 78$ . Use the formula $s = \sqrt{\frac{\sum(x-\bar{x})^{2}}{n-1}}$ .

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Problem 259

Calculate the correlation coefficient $r$ for the given $\mathbf{x}$ and $\mathbf{y}$ data. Round the result to two decimal places.

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Problem 260

Find the percentage of athletes who took more than $24 \mathrm{s}$ to finish a $200 \mathrm{~m}$ race, given the time distribution in the table.

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Problem 261

The mean age of lead actors from the top ten grossing movies of 2007 was $36.4$ years with a standard deviation of $9.87$ years. Assume the distribution is approximately unimodal and symmetric. According to the Empirical Rule, the ages of nearly all lead actors will be between $\$16.7 ; 56.1\$$ years. Adrien Brody, who was 29 years old when he won the academy award in 2002, was within this range.

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Problem 262

Generate a scatter plot with regression equation $y=32.73x+15.14$ and $r=0.044$ . What proportion of variation in $y$ can be explained by the regression? Round to 3 decimals. What is the symbol for this calculation? What is this term called?

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Problem 263

The company retires cars based on miles, purpose, and style. The car fleet's service duration follows a normal distribution with $\mu=62$ months and $\sigma=5$ months. What is the approximate percentage of cars in service between 47 and 57 months?

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Problem 264

The university's physical plant receives daily requests to replace fluorescent lightbulbs. The distribution of requests follows a normal distribution with $\mu=59$ and $\sigma=10$ . Using the Empirical Rule, find the percentage of requests between 39 and 59.
ans = 68.27%

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Problem 265

Which of the following statements about a normal distribution are true? $\mu = \text{mode} = \text{median}$

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Problem 266

Calculate the standard error of the sample proportion $\hat{p}$ for $n=100$ and various values of $p$ . Observe how the standard error changes as $p$ approaches 0 or 1.

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Problem 267

Find the degrees of freedom, critical values $\chi_{L}^{2}$ and $\chi_{R}^{2}$ , and $\sigma$ confidence interval for a normal distribution sample with $n=149, s=1.95$ (1000 cells/ $\mu \mathrm{L}$ ) at 99% confidence.

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Problem 268

The standard deviation is the square root of the variance.

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Problem 269

Rewrite interval with given values: $\hat{p} = 0.61, z^* = 0.82, SE_{\text{est}} = 0.00157$ . The interval is $[0.607, 0.613]$ .

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Problem 270

Engineers must design helmets to fit the normal distribution of male head breadths with $\mu = 6.1$ -in and $\sigma = 1.2$ -in.
Find the middle $99\%$ of head breadths: Between $3.71$ -in and $8.49$ -in.
Find the middle $99\%$ of sample averages for head breadths of size $60$ : Between $5.86$ -in and $6.34$ -in.

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Problem 271

Find the number of oranges between 3 oz and 5 oz in a batch of 2300, given a normal distribution with $\mu = 6$ oz and $\sigma = 1.5$ oz.

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Problem 272

Determine if half of all teens aged 13-17 have made new friends online using a 0.05 significance level and the normal distribution.
$H_0: p = 0.5$ $H_1: p \neq 0.5$

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Problem 273

Polygraph experiment has 99 results: 22 wrong, 77 correct. Test if correct results are <80% using 0.05 significance. Find null/alt hypotheses, test statistic, P-value, conclusion.
$H_0: p = 0.80, H_1: p < 0.80$ Test statistic $z = -0.55$ P-value = 0.2912 (rounded to four decimal places)

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Problem 274

Determine the total number of subjects, the number who did not use marijuana, and the probability a random subject did not use marijuana given drug test results.
Total subjects: $\square$ Subjects who did not use marijuana: $\square$ Probability a random subject did not use marijuana: $\square$

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Problem 275

Find the 25th and 90th percentiles of serum cholesterol levels (mg/dL) for 15 individuals: $198, 259, 196, 249, 186, 240, 208, 222, 218, 191, 244, 257, 254, 211, 189$ . (a) 25th percentile: $[\frac{\mathrm{mg}}{\mathrm{dL}}]$ . (b) 90th percentile: $\square \frac{\mathrm{mg}}{\mathrm{dL}}$ .

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Problem 276

In Alabama, 44% of the population favors the incumbent for governor. Find the probability that at least 72 out of 150 randomly sampled respondents favor the incumbent, using a normal approximation with continuity correction.
$X \sim \text{Binomial}(n=150, p=0.44)$
$P(X \geq 72)$
$Y \sim \text{Normal}(\mu=66, \sigma=5.24)$
$P(Y \geq 71.5)$
Use continuity correction
Probability: 0.8001

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Problem 277

Estimate the proportion of oil tankers that had spills given a sample of 712 tankers, where 570 did not have spills. Enter the result as a fraction or decimal rounded to 3 decimal places.

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Problem 278

Determine the tire lifespan warranty that will replace no more than $10\%$ of tires, given a normal distribution with $\mu=47,700$ miles and $\sigma=2,000$ miles.

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Problem 279

Find the number of classes and their lower/upper class limits given the minimum, maximum, and class width.
$\text{minimum} = 9, \text{maximum} = 80, \text{number of classes} = 7$
The class width is $11$ . Find the lower class limits and upper class limits.

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Problem 280

Find the modes of the sibling count data: $1, 2, 4, 0, 3$ .

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Problem 281

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided $2 \times 4$ contingency table.

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Problem 282

Find the expected value of a randomly chosen student's score on last year's final exam given the score distribution.
$X$ = score of a randomly chosen student Expected value of $X$ = $\frac{(19 \times 3) + (35 \times 3) + (60 \times 4)}{10}$

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Problem 283

Find the mean, median, and mode of the test scores: $84, 79, 77, 73, 79, 65, 75$ .

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Problem 284

Find the average of the numbers $16, 8, 21, 16$ . Round to one decimal place if necessary.

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Problem 285

Construct a grouped frequency distribution for the ages of presidents at inauguration, using classes of width 5 starting from 41-45. Provide the frequency value for each class.
$41 - 45: \square$ $46 - 50: \square$ $51 - 55: \square$ $56 - 60: \square$ $61 - 65: \square$ $66 - 70: \square$

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Problem 286

Determine the number of college students who got news from only social media using a Venn diagram. Given: 94 students surveyed, 32 from news websites, 25 from social media, and 11 from both.
$n($ News websites only $)=21$ $n($ Social media only $)=\boxed{14}$

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Problem 287

Determine the sample size needed to estimate the proportion of a population with a genetic marker, with 99% confidence and 1.5% margin of error, given the expected proportion is 80%.
$n = \frac{z^{2}_{\alpha/2} p^{} (1 - p^{})}{E^{2}}$

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Problem 288

Find the critical t-value for a 90% confidence level with a sample size of 11.

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Problem 289

Find the midquartile of football league passer ratings, where Midquartile = $(Q_{1} + Q_{3})/2$ . The ratings are: 99.7, 95.7, 89.2, 84.7, 83.3, 82.4, 78.5, 77.8, 76.3, 74.4.

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Problem 290

Determine the mean and standard deviation of the sampling distribution of the proportion of voters supporting a candidate in a county, given the population proportion and sample size.
Mean: $\mu_{\widehat{p}}=0.2700$ Standard error: $\sigma_{\widehat{p}}=0.0226$

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Problem 291

Find the possible p-value if the null hypothesis is rejected at $\alpha=0.05$ .

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Problem 292

Find $x$ using the $z$ -score formula $z=\frac{x-\mu}{\sigma}$ with $z=4.25$ , $\mu=14.4$ , $\sigma=3.6$ . Round to 1 decimal place.

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Problem 293

Poisson regression uses PMF $p(y \mid \lambda)=\frac{\lambda^{y}}{y !} e^{-\lambda}$ .
1. Find loss $\ell_{i}(\beta)$ and its gradient.
2. Prove $R_{n}(\beta)$ is convex.
3. Show $F_{\eta}(\hat{\beta})=\hat{\beta}$ at minimizer.
4. Implement gradient descent to estimate $\hat{\beta}$ and compare with true $\beta$ .

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1 2 3

Statistics

Problem 201

A survey asked students to rate their stress level from 0 (not stressed) to 10 (very stressed). Find the most common stress rating.

Problem 202

Find the five-number summary and interquartile range for the given temperatures in 51,54,56,58,61,61,69,72,80,81,8451, 54, 56, 58, 61, 61, 69, 72, 80, 81, 8451,54,56,58,61,61,69,72,80,81,84 Fahrenheit.

Problem 203

Find the most frequently occurring value in the data set: 20,31,46,31,49,31,4920, 31, 46, 31, 49, 31, 4920,31,46,31,49,31,49.

Problem 204

Determine if the statement "When finding the \mean, it is necessary to arrange the data items in order" is true or false. Provide the correct answer.

Problem 205

A sample of n=25n=25n=25 produces t=2.062t=2.062t=2.062. Researcher can reject null hypothesis with α=.05\alpha=.05α=.05 but not α=.01\alpha=.01α=.01 using two-tailed test.

Problem 206

Problem 207

Find the probability a student without an A is female given the gender and grade data for the class.P(Female∣No A)=P(No A∩Female)P(No A)P(\text{Female} | \text{No A}) = \frac{P(\text{No A} \cap \text{Female})}{P(\text{No A})}P(Female∣No A)=P(No A)P(No A∩Female)​

Problem 208

Probability that a student who did not complete homework passed a test, given data table of students who passed/failed test and completed/did not complete homework.

Problem 209

Find the mean of the corrected list of elapsed times: 2.16,2.88,2.96,2.09,2.64,2.36,2.222.16, 2.88, 2.96, 2.09, 2.64, 2.36, 2.222.16,2.88,2.96,2.09,2.64,2.36,2.22.

Problem 210

Find total variation for predicted data (0,8),(1,5),(2,2)(0,8), (1,5), (2,2)(0,8),(1,5),(2,2) from line of best fit y′=8−3xy' = 8 - 3xy′=8−3x. Provide actual observed data points to calculate total variation.

Problem 211

Find the 5 number summary for the data: 93,42,9,12,86,10,43,53,89,49,5593, 42, 9, 12, 86, 10, 43, 53, 89, 49, 5593,42,9,12,86,10,43,53,89,49,55.

Problem 212

Find the regression with the weakest linear relationship between x\mathrm{x}x and y\mathrm{y}y given y=ax+by=a x+by=ax+b with aaa and bbb values and correlation coefficient rrr.

Problem 213

Problem 214

Find the residual value for the coordinate (4,9) given the line of best fit y=1.18x+5.4y=1.18x+5.4y=1.18x+5.4. Options: 0.860.860.86, −0.86-0.86−0.86, 1.121.121.12, −1.12-1.12−1.12

Problem 215

Compute the mean, median, and mode of repair costs for 4 crashes of the same car model at 5 mph. The repair costs are 429,429, 429,448, 486,and486, and 486,and222. A. The mean cost of repair is $396.25\$ 396.25$396.25. (Round to the nearest cent as needed.)

Problem 216

Find the probability that a randomly chosen 10-year-old in the US has height between 39.939.939.9 and 46.446.446.4 inches, given heights are normally distributed with mean 55.755.755.7 inches and standard deviation 999 inches. Round final answer to 3 decimal places.

Problem 217

Around what percentage of adults in the USA have stage 2 high blood pressure (SBP≥160\text{SBP} \geq 160SBP≥160) given that SBP is normally distributed with μ=122\mu=122μ=122 and σ=16\sigma=16σ=16? Round to two decimal places.

Problem 218

Estimate 51 marbles in a jar, actual is 42. Find the percent error, rounded to the nearest tenth.

Problem 219

Calculate the sample variance for the set of numbers: 10,90,91,85,5710, 90, 91, 85, 5710,90,91,85,57. Round the result to 2 decimal places.

Problem 220

Find the percentage of data to the left of the z-score z=1.05z=1.05z=1.05.

Problem 221

Find the five-number summary and interquartile range for the distances (in miles) to the nearest airport for 11 families: 8,13,19,19,21,23,28,28,31,37,428, 13, 19, 19, 21, 23, 28, 28, 31, 37, 428,13,19,19,21,23,28,28,31,37,42.

Problem 222

What is the unemployment rate if the job separation rate is 0.050.050.05 and the job finding rate is 0.350.350.35?

Problem 223

Calculate the sample standard deviation of ages in a dataset of 23, 62, 22, 67. The closest approximation is 2102 \sqrt{10}210​.

Problem 224

Evaluate time series model for quarterly raincoat sales data (2010-2015) in London. Determine if statements about Y=T+S+EY = T + S + EY=T+S+E model are true or false.

Problem 225

Find the median weight of a sample of 13 male 11th graders with weights 152,165,140,150,175,142,172,171,156,158,168,146,160152, 165, 140, 150, 175, 142, 172, 171, 156, 158, 168, 146, 160152,165,140,150,175,142,172,171,156,158,168,146,160 pounds.

Problem 226

Find the range of the sound loudness estimates (in decibels) with a mean of 707070: 68,67,70,71,68,75,68,62,80,73,6868, 67, 70, 71, 68, 75, 68, 62, 80, 73, 6868,67,70,71,68,75,68,62,80,73,68.

Problem 227

Find the probability that Victoria's next bowling score, which is normally distributed with μ=130\mu=130μ=130 and σ=11\sigma=11σ=11, falls between 123 and 130. Round the answer to the nearest whole percent.

Problem 228

Add missing values to incomplete box plot using data set: 81,83,83,83,84,84,84,84,85,86,87,8881, 83, 83, 83, 84, 84, 84, 84, 85, 86, 87, 8881,83,83,83,84,84,84,84,85,86,87,88.

Problem 229

Find the range of the caterpillar cocoon days: 8,12,5,9,21,18,9,78, 12, 5, 9, 21, 18, 9, 78,12,5,9,21,18,9,7.

Problem 230

Find the range of pregnancy lengths that covers the middle 95% of pregnancies in a village, given a normal distribution with μ=200\mu = 200μ=200 days and σ=15\sigma = 15σ=15 days.

Problem 231

Problem 232

Find the xxx-value that separates the top 12% of a normal distribution with μ=52.1,σ=7.5\mu=52.1, \sigma=7.5μ=52.1,σ=7.5 from the rest of the data.

Problem 233

Chemical engineer must report the average volume of a pollutant produced by plants. Data: Platte 2.7722.7722.772 L, Macon 48.5848.5848.58 L, South Fork 2.362.362.36 L. What average volume should be reported with correct significant digits?

Problem 234

Find the correlation coefficient rrr between X\boldsymbol{X}X and y\boldsymbol{y}y given ∑(x−xˉ)(y−yˉ)=11\sum(x-\bar{x})(y-\bar{y})=11∑(x−xˉ)(y−yˉ​)=11, σx=3.62\sigma_x=3.62σx​=3.62, σy=3.23\sigma_y=3.23σy​=3.23, and n=16n=16n=16.

Problem 235

Which measure of central tendency is most affected by the extreme value in the given half marathon pace data?{6.7,7.1,7.5,7.6,3.3,7.4,7.2,7.4,7.1,7.4,6.8,6.9,7.3}\{6.7, 7.1, 7.5, 7.6, 3.3, 7.4, 7.2, 7.4, 7.1, 7.4, 6.8, 6.9, 7.3\}{6.7,7.1,7.5,7.6,3.3,7.4,7.2,7.4,7.1,7.4,6.8,6.9,7.3}

Problem 236

Problem 237

Identify the levels of measurement: {\{{Nominal Data, Ratio, Quantitative Data, Ordinal Data}\}}

Problem 238

Determine if the underlined value, 59%59\%59% of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

Problem 239

Problem 240

Problem 241

Find the 98th percentile of a standard normal distribution with mean 0 and standard deviation 1.

Problem 242

Calculate the range, variance, and standard deviation for the given samples. a. 34,47,45,40,4834, 47, 45, 40, 4834,47,45,40,48, b. 100,3,9160,16207100, 3, 9160, 16207100,3,9160,16207, c. 100,35,40,6040,447100, 35, 40, 6040, 447100,35,40,6040,447. a. The range is □\square□.

Problem 243

Find the five-number summary and interquartile range for the given temperatures in $51, 54, 56, 58, 61, 61, 69, 72, 80, 81, 84$ Fahrenheit.

Find the most frequently occurring value in the data set: $20, 31, 46, 31, 49, 31, 49$ .

A sample of $n=25$ produces $t=2.062$ . Researcher can reject null hypothesis with $\alpha=.05$ but not $\alpha=.01$ using two-tailed test.

Find the probability a student without an A is female given the gender and grade data for the class.
$P(\text{Female} | \text{No A}) = \frac{P(\text{No A} \cap \text{Female})}{P(\text{No A})}$

Find the mean of the corrected list of elapsed times: $2.16, 2.88, 2.96, 2.09, 2.64, 2.36, 2.22$ .

Find total variation for predicted data $(0,8), (1,5), (2,2)$ from line of best fit $y' = 8 - 3x$ . Provide actual observed data points to calculate total variation.

Find the 5 number summary for the data: $93, 42, 9, 12, 86, 10, 43, 53, 89, 49, 55$ .

Find the regression with the weakest linear relationship between $\mathrm{x}$ and $\mathrm{y}$ given $y=a x+b$ with $a$ and $b$ values and correlation coefficient $r$ .

Find the residual value for the coordinate (4,9) given the line of best fit $y=1.18x+5.4$ . Options: $0.86$ , $-0.86$ , $1.12$ , $-1.12$

Compute the mean, median, and mode of repair costs for 4 crashes of the same car model at 5 mph. The repair costs are $429,$ 448, $486, and$ 222. A. The mean cost of repair is $\$ 396.25$ . (Round to the nearest cent as needed.)

Find the probability that a randomly chosen 10-year-old in the US has height between $39.9$ and $46.4$ inches, given heights are normally distributed with mean $55.7$ inches and standard deviation $9$ inches. Round final answer to 3 decimal places.

Around what percentage of adults in the USA have stage 2 high blood pressure ( $\text{SBP} \geq 160$ ) given that SBP is normally distributed with $\mu=122$ and $\sigma=16$ ? Round to two decimal places.

Calculate the sample variance for the set of numbers: $10, 90, 91, 85, 57$ . Round the result to 2 decimal places.

Find the percentage of data to the left of the z-score $z=1.05$ .

Find the five-number summary and interquartile range for the distances (in miles) to the nearest airport for 11 families: $8, 13, 19, 19, 21, 23, 28, 28, 31, 37, 42$ .

What is the unemployment rate if the job separation rate is $0.05$ and the job finding rate is $0.35$ ?

Calculate the sample standard deviation of ages in a dataset of 23, 62, 22, 67. The closest approximation is $2 \sqrt{10}$ .

Evaluate time series model for quarterly raincoat sales data (2010-2015) in London. Determine if statements about $Y = T + S + E$ model are true or false.

Find the median weight of a sample of 13 male 11th graders with weights $152, 165, 140, 150, 175, 142, 172, 171, 156, 158, 168, 146, 160$ pounds.

Find the range of the sound loudness estimates (in decibels) with a mean of $70$ : $68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68$ .

Find the probability that Victoria's next bowling score, which is normally distributed with $\mu=130$ and $\sigma=11$ , falls between 123 and 130. Round the answer to the nearest whole percent.

Add missing values to incomplete box plot using data set: $81, 83, 83, 83, 84, 84, 84, 84, 85, 86, 87, 88$ .

Find the range of the caterpillar cocoon days: $8, 12, 5, 9, 21, 18, 9, 7$ .

Find the range of pregnancy lengths that covers the middle 95% of pregnancies in a village, given a normal distribution with $\mu = 200$ days and $\sigma = 15$ days.

Find the $x$ -value that separates the top 12% of a normal distribution with $\mu=52.1, \sigma=7.5$ from the rest of the data.

Chemical engineer must report the average volume of a pollutant produced by plants. Data: Platte $2.772$ L, Macon $48.58$ L, South Fork $2.36$ L. What average volume should be reported with correct significant digits?

Find the correlation coefficient $r$ between $\boldsymbol{X}$ and $\boldsymbol{y}$ given $\sum(x-\bar{x})(y-\bar{y})=11$ , $\sigma_x=3.62$ , $\sigma_y=3.23$ , and $n=16$ .

Which measure of central tendency is most affected by the extreme value in the given half marathon pace data?
$\{6.7, 7.1, 7.5, 7.6, 3.3, 7.4, 7.2, 7.4, 7.1, 7.4, 6.8, 6.9, 7.3\}$

Identify the levels of measurement: $\{$ Nominal Data, Ratio, Quantitative Data, Ordinal Data $\}$

Determine if the underlined value, $59\%$ of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

Calculate the range, variance, and standard deviation for the given samples. a. $34, 47, 45, 40, 48$ , b. $100, 3, 9160, 16207$ , c. $100, 35, 40, 6040, 447$ . a. The range is $\square$ .

Find the mode of the sample scores $[4, 14, 56, 0.8, 14, 56, 14]$ .

Calculate the standard deviation of the distances (in miles) traveled to work by 5 employees: $10, 3, 14, 34, 9$ . Round the answer to two decimal places.

Find the total number of registered doctors if $33.6\%$ were female and there were 48,200 female registered doctors.

Given normal calorie burn data with $\mu=310$ and $\sigma=7$ , find probabilities of: (a) >320 calories, (b) <302 calories, (c) 298-330 calories. The probability of (b) is $12.70\%$ , and the probability of (c) is $\square$ .

Determine the most accurate and precise measurements of signal speed in a nerve fiber, given a later reliable measurement of $16.0 \mathrm{~m} / \mathrm{s}$ and four teams' earlier measurements.

Find the average of the numbers $49, 78, 64, 61, 69, 29, 70, 24, 25, 40, 33, 20, 35, 34$ .

Approximate the mean gas mileage (in miles per gallon) from a frequency distribution of 23 cars. Round the mean to one decimal place.
$25-30: 9, 31-36: 10, 37-42: 1, 43-48: 3$

Find the missing value $x$ in the set $\{4, 16, 14, x, 10\}$ if the mean is 12.

A manufacturer's item lengths are normally distributed with $\mu = 14.2$ inches and $\sigma = 2.3$ inches. Find the probability that the mean length of 35 randomly chosen items exceeds 13.6 inches. (Round to 4 decimal places)

Determine the standard deviation of the number of people with a $6\%$ genetic mutation in a random sample of 600 individuals. Round to 3 decimal places.

Find the mean, median, and mode(s) of the data set $54, 44, 38, 40, 49, 43, 52, 45, 31, 35$ . Round the mean and median to one decimal place if necessary.

Calculate the standard deviation of the marks of 9 students: $71, 58, 89, 93, 91, 53, 56, 86, 78$ . Use the formula $s = \sqrt{\frac{\sum(x-\bar{x})^{2}}{n-1}}$ .

Calculate the correlation coefficient $r$ for the given $\mathbf{x}$ and $\mathbf{y}$ data. Round the result to two decimal places.

Find the percentage of athletes who took more than $24 \mathrm{s}$ to finish a $200 \mathrm{~m}$ race, given the time distribution in the table.

Generate a scatter plot with regression equation $y=32.73x+15.14$ and $r=0.044$ . What proportion of variation in $y$ can be explained by the regression? Round to 3 decimals. What is the symbol for this calculation? What is this term called?

The company retires cars based on miles, purpose, and style. The car fleet's service duration follows a normal distribution with $\mu=62$ months and $\sigma=5$ months. What is the approximate percentage of cars in service between 47 and 57 months?

The university's physical plant receives daily requests to replace fluorescent lightbulbs. The distribution of requests follows a normal distribution with $\mu=59$ and $\sigma=10$ . Using the Empirical Rule, find the percentage of requests between 39 and 59.
ans = 68.27%

Which of the following statements about a normal distribution are true? $\mu = \text{mode} = \text{median}$

Calculate the standard error of the sample proportion $\hat{p}$ for $n=100$ and various values of $p$ . Observe how the standard error changes as $p$ approaches 0 or 1.

Find the degrees of freedom, critical values $\chi_{L}^{2}$ and $\chi_{R}^{2}$ , and $\sigma$ confidence interval for a normal distribution sample with $n=149, s=1.95$ (1000 cells/ $\mu \mathrm{L}$ ) at 99% confidence.

Rewrite interval with given values: $\hat{p} = 0.61, z^* = 0.82, SE_{\text{est}} = 0.00157$ . The interval is $[0.607, 0.613]$ .

Find the number of oranges between 3 oz and 5 oz in a batch of 2300, given a normal distribution with $\mu = 6$ oz and $\sigma = 1.5$ oz.

Determine if half of all teens aged 13-17 have made new friends online using a 0.05 significance level and the normal distribution.
$H_0: p = 0.5$ $H_1: p \neq 0.5$