Measures of Spread

Problem 1

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

See Solution

Problem 2

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

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Problem 3

Um zootecnista testa nova ração para coelhos. Qual média deve ser superior para trocar a ração atual? (A) 5,0 (B) 9,5 (C) 10,0 (D) 10,5 (E) 15,0.

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Problem 4

Find scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

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Problem 5

Find the score's location $x$ from the mean using standard deviation for these cases: a. $x=31.2$ , $\mu=23.5$ , $\sigma=8.3$ ; b. $x=151.4$ , $\mu=187.4$ , $\sigma=50.1$ ; c. $x=301.21$ , $\mu=257.89$ , $\sigma=34.71$ .

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Problem 6

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

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Problem 7

Find the mean and standard deviation for these data sets: a. Set $A$ : below 12.3, above 17.8. b. Set $B$ : below 3.51, above 41.16. c. Set $C$ : below 12.41, above 35.12.

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Problem 8

Check if $X$ is an outlier for these sets: a. $\mu=12.3, \sigma=2.1, X=8.0$ b. $\mu=21.75, \sigma=7.4, X=15.13$ c. $\mu=51.13, \sigma=5.41, X=41.75$ d. $\mu=14.13, \sigma=1.3, X=10.1$

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Problem 9

Describe a distribution that is NOT normally distributed.

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Problem 10

Find the scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

See Solution

Problem 11

Calculate the inflation rate from 2015 to 2016 using CPI: $\text{Inflation Rate} = \frac{CPI_{2016} - CPI_{2015}}{CPI_{2015}} \times 100$

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Problem 12

Mike wants to evaluate Hi-Tech Inc. stock. Calculate annual returns from 2009 to 2012, find standard deviation, and determine if the coefficient of variation is below 0.90 for investment.

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Problem 13

Jamie Wong wants to build a portfolio with stocks L (40%) and M (60%). Calculate:
a. Expected return $r_{p}$ for each year (2013-2018). b. Average return $\bar{r}_{p}$ over 6 years. c. Standard deviation $\sigma_{r_{p}}$ over 6 years. d. Correlation of returns for stocks L and M. e. Benefits of diversification in the portfolio.

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Problem 14

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return $r_{p}$ , b) average return $\bar{r}_{p}$ , c) standard deviation $\sigma_{r_{p}}$ , d) correlation of returns, e) diversification benefits.

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Problem 15

Find the relative error of a car's speed measured as $48 \mathrm{~km} / \mathrm{h}$ , rounded to the nearest $\mathrm{km} / \mathrm{h}$ .

See Solution

Problem 16

A jogging track is $500 \mathrm{~m}$ long with a $0.1 \%$ error. What is the scale interval of the measuring tool?

See Solution

Problem 17

Find the max absolute error, measured time, and percentage error for $t$ with $25.465 \leq t < 25.475$ .

See Solution

Problem 18

Find the percentage error in measuring an elephant's weight, capped at $5825 \mathrm{~kg}$ , with a $10 \mathrm{~kg}$ scale.

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Problem 19

Find the score's position $x$ relative to the mean using standard deviation for: a. $x=31.2$ , $\mu=23.5$ , $\sigma=8.3$ ; b. $x=151.4$ , $\mu=187.4$ , $\sigma=50.1$ ; c. $x=301.21$ , $\mu=257.89$ , $\sigma=34.71$ .

See Solution

Problem 20

Find how many standard deviations each score $x$ is from the mean $\mu$ for the given distributions.

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Problem 21

Find the $Z$ -score for these Math test scores: mean = 36, standard deviation = 8. Scores: 26, 39, 42, 32, 37.

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Problem 22

Find the $Z$ -score for a student who scored 74 on a test with an average of 80 and a standard deviation of 6.

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Problem 23

Determine if a 100-m dash time of 24.7 seconds is satisfactory given $\mu=28.5$ and $\sigma=3.1$ .

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Problem 24

Check if $X$ is an outlier using $\mu$ and $\sigma$ for these scores: a. $X=8.0$ , $\mu=12.3$ , $\sigma=2.1$ ; b. $X=15.13$ , $\mu=21.75$ , $\sigma=7.4$ ; c. $X=41.75$ , $\mu=51.13$ , $\sigma=5.41$ ; d. $X=10.1$ , $\mu=14.13$ , $\sigma=1.3$ .

See Solution

Problem 25

Find Patrick's $Z$ -score if he scored 85 on a test with a mean of 100 and a standard deviation of 15.

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Problem 26

Evaluate investments X, Y, Z against a return of $12\%$ and $6\%$ SD. Choose based on risk preferences: neutral, averse, seeking.

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Problem 27

Sharon Smith evaluates investments X, Y, Z against a 12% return and 6% risk. Determine selections for risk neutral, averse, and seeking.

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Problem 28

Find the $\mathrm{z}$ -score for $\mathrm{x}=7$ given that the mean of $\mathrm{X}$ is 4 and the standard deviation is 2.

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Problem 29

Find the $\mathrm{z}$ -score for $\mathrm{x}=7$ given that the mean of $\mathrm{X}$ is 4 and standard deviation is 2.

See Solution

Problem 30

Find the skewness ( $=4.217$ ) and kurtosis ( $=18.342$ ) of the data and describe the distribution shape.

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Problem 31

Find the class width if the range is 71.4, measurement unit is 0.001, and there are 10 classes.

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Problem 32

A pencil measures $7.50 \, \text{cm}$ . Find (a) max absolute error, (b) relative error, (c) percentage error. Use 3 sig. figs.

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Problem 33

Calculate the average return, covariance, and correlation coefficient for Merias and Gangnam based on their monthly returns.

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Problem 34

Find a $99\%$ confidence interval for the standard deviation $\sigma$ of washing machine replacement times from a sample of 20, with mean 11.6 and SD 2.2. Calculate $\chi_{L}^{2}$ , $\chi_{R}^{2}$ , and interpret the interval.

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Problem 35

For males, systolic blood pressure is normal with mean 120 and SD 5. Find the interval for the middle $68\%$ .

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Problem 36

Find the systolic blood pressure range for the middle $99.7\%$ of males, given a mean of 105 and SD of 10.

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Problem 37

Find the z-score for a person who scored 26 on an exam with a mean of 24 and a standard deviation of 4.

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Problem 38

Find the systolic blood pressure range for the middle $99.7\%$ of males, given mean $125$ and SD $7$ .

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Problem 39

Find the z-score for a person who scored 128 on a test with a mean of 100 and a standard deviation of 10: $z = \frac{128 - 100}{10}$ .

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Problem 40

Find the z-score for a score of 47 on a test with a mean of 36 and standard deviation of 4. Use $z = \frac{x - \mu}{\sigma}$ .

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Problem 41

Find the z-score for a score of 160 on a standardized exam where the mean is 135 and the standard deviation is 25.

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Problem 42

Find the z-score for a score of 350 on a normal distribution with mean 300 and standard deviation 40.

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Problem 43

Find the z-score for a score of 210, given a mean of 200 and a standard deviation of 20. Use $z = \frac{x - \mu}{\sigma}$ .

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Problem 44

Calculate the interquartile range for these data sets: Set 1: 21, 5, 14, 10, 8, 17, 2 Set 2: 27, 26, 31, 23, 28, 32, 26 Which set has an interquartile range indicating data is closer to the median?

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Problem 45

Find the interquartile range of the data set: 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81. A. 62 B. 21 C. 79 D. 41

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Problem 46

Find the standard deviation of ACT scores, mean = 21.5, with 19% above 25. Round to the nearest tenth.

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Problem 47

Sharon Smith evaluates investments X, Y, Z against a 12% return, 6% std. dev. Select investments for risk neutral, averse, and seeking.

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Problem 48

Solar Designs is evaluating two expansions. Find the return ranges, assess risk, choose an investment, and analyze changes if rates shift.

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Problem 49

Solar Designs is evaluating two expansions. Determine the return range for each, assess risk, and choose an investment.

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Problem 50

Find the standard deviation of human pregnancy lengths given a mean of 267 days and $95\%$ lasting between 245 and 289 days. What percent last at least 285 days? Standard deviation: $\square$ days.

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Problem 51

Find the cutoff score for an $A$ if the mean is 74 and the standard deviation is 8.11, top $6\%$ .

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Problem 52

Calculate the coefficient of variation for four production alternatives with returns and standard deviations. Recommend the best option to minimize risk.

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Problem 53

Greengage, Inc. is evaluating four projects. Determine the least risky by range, lowest standard deviation, and calculate the coefficient of variation for each project. Which project should they choose?

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Problem 54

Swift Manufacturing evaluates two projects. Find the return range, expected return, standard deviation, and coefficient of variation for each project. Also, create bar charts for the returns and determine which project is less risky.

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Problem 55

Find the confidence interval for the true mean weight given a mean of 167 pounds and a margin of error of 3 pounds.

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Problem 56

Calculate the expected return $r_{p}$ for a portfolio of stocks L (40\%) and M (60\%) over 2013-2018, then find $\bar{r}_{p}$ and $\sigma_{r_{p}}$ . Discuss correlation and diversification benefits.

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Problem 57

Find a reasonable value for the true mean weight of residents if the mean is 197 pounds with a margin of error of 9 pounds.

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Problem 58

Find the confidence interval for the true mean SAT score given a mean of 449 and a margin of error of 18.

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Problem 59

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate expected return, average return, std. dev., correlation, and diversification benefits.

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Problem 60

Find the confidence interval for the mean SAT score given a mean of 454 and a margin of error of 27.

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Problem 61

Find the interquartile range of the following heights (in inches): 5'4", 6'2", 6', 5'4", 5'4", 5'3", 5'5", 5'6", 5'4", 5'3".

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Problem 62

Analyze expected returns and risks for three investment alternatives using data from assets F, G, and H from 2013-2016. Calculate returns, standard deviations, and coefficients of variation. Recommend the best alternative.

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Problem 63

Survey shows $56\%$ in favor and $44\%$ opposed to a garage sale. Find least and greatest percent opposed ( $\pm 5\%$ ). Is half the town opposed? Explain.

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Problem 64

Describe the distribution of ages for club members given the data: 5: 0, 7, 8; 6: 1, 2, 3, 3, 4, 6, 9; 7: 0, 1, 4, 5, 8, 9; 8: 0, 2.

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Problem 65

How many police officers in 2016 must exceed the private investigators' percent increase from 52,000 to 61,000? Options: a. 657,983 b. 761,307 c. 671,128 d. 713,180

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Problem 66

Which job will see the highest percent increase in employment from 2006 to 2016: Orthodontist, Sound engineer technician, Police officer, or Editor?

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Problem 67

Find the interquartile range of the data set: $10, 3, 7, 6, 9, 12, 13$ .

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Problem 68

Find the least value among the median, mean, and range of these numbers: 11, 24, 37, 38, 41, 46.

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Problem 69

Create a box and whisker plot for the heights: 62, 63, 64, 64, 66, 67, 68, 72, 72, 74, 75, 76. Find the interquartile range.

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Problem 70

Calculate the standard deviation and variance of the data: 16.3, 1.7, 28, 9.2, 15.2, 26.1, 8.5, 20.4.

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Problem 71

Calculate the sample and population standard deviations for the data: 22, 25, 21, 11, 15, 29. Round to two decimals.

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Problem 72

Find the min, max, range, mean (to 2 decimals), and standard deviation of TV hours for 24 kids: 77, 38, 35, 54, 30, 32, 85, 12, 70, 91, 25, 71, 95, 90, 99, 11, 66, 74, 90, 78, 34, 77, 39, 62.

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Problem 73

Calculate the sample standard deviation for the aptitude scores with frequencies: 0 (2), 1 (6), 2 (0), 3 (0), 4 (3), 5 (4).

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Problem 74

Calculate the sample standard deviation of the following musical aptitude scores: 0 (3), 1 (3), 2 (1), 3 (8), 4 (3), 5 (5).

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Problem 75

Find the five-number summary (min, Q1, median, Q3, max) for the dataset: 53, 18, 54, 65, 48, 70, 38, 63, 28, 41, 45, 33, 52, 20, 43, 23, 30, 79, 42, 89.

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Problem 76

Find the five-number summary (min, Q1, median, Q3, max) for the data set: 25, 53, 81, 60, 54, 46, 13, 52, 43, 39, 36, 10, 41, 37, 77, 57, 56.

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Problem 77

Find the five-number summary and IQR for the data: 25, 53, 81, 60, 54, 46, 13, 52, 43, 39, 36, 10, 41, 37, 77, 57, 56. Identify outlier bounds and any outliers.

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Problem 78

Find the five number summary, range, and interquartile range from the given stem & leaf plot data.

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Problem 79

Find the five-number summary for the data: 25, 53, 81, 60, 54, 46, 13, 52, 43, 39, 36, 10, 41, 37, 77, 57, 56. Determine IQR, lower & upper outlier bounds, and any outliers.

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Problem 80

Find the five-number summary for the data: 10, 12, 21, 35, 36, 41, 42, 43, 44, 46, 47, 49, 52, 58, 59, 60, 83, 88. Calculate IQR, outlier bounds, and any outliers.

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Problem 81

In a group of 348 students, how many will have an IQ within 1 standard deviation (15) of the mean (100)?

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Problem 82

What percentage of a sample is above 3 standard deviations from the mean according to the empirical rule? a. 2.5 b. 0.5 c. 1 d. 2

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Problem 83

How many students have IQs > 100? Also, what % of a sample is within one standard deviation below the mean?

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Problem 84

Lisetta's new temperature lowers the standard deviation. What can we conclude about today's temperature compared to the previous 10 days?

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Problem 85

Eileen has a data set with 12 values and a standard deviation of 0. What must be true? Select all that apply.

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Problem 86

Sandy analyzes teen wages, calculates mean, median, and standard deviation, then compares original and raised by \$2/hr.

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Problem 87

Find the variance and standard deviation of this dataset: 1.00, 2.40, 3.60, 4.45, 4.50, 5.56, 6.89, 7.33, 8.99, 10.00.

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Problem 88

Find the variance and standard deviation of this dataset: 1.00, 2.40, 3.60, 4.45, 4.50, 5.56, 6.89, 7.33, 8.99, 10.00. Options: a) 4.02, 1.12 b) 4.78, 2.21 c) 5.03, 1.35 d) 8.14, 2.85.

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Problem 89

Find the $z$ -score for a 90-pound dog given an average weight of 84 pounds and a standard deviation of 4 pounds.

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Problem 90

Which score from the set $10, 20, 30, 40, 50, 60$ has a z score of 0.00? Choices: 10, 20, 30, 35, 50.

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Problem 91

Find how many standard deviations above the mean a person with a $1 \mathrm{Q}$ of 130 scores.

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Problem 92

Calculate the mean absolute deviation of the values 4, 15, 16, 7, 5, 19. Round to the nearest hundredth if needed.

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Problem 93

Find the standard deviation of the monthly salaries (in \ $1000s):$ 8, 13, 11, 12, 6, 10$. Round to two decimal places.

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Problem 94

Calculate the absolute and relative changes in Japan's population under 15 from 1980 (18.08\%) to 2020 (12.45\%).

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Problem 95

Calculate the range of the following traveler spending data (in billions): $20.9, 33.1, 21.8, 58.5, 23.5, 110.9, 30.4, 24.9, 74.1, 60.3, 40.4, 45.4$ . Round to two decimal places.

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Problem 96

Two groups measure fall times for a ball. Find averages, percentage errors, standard deviations, and variances. Round to two decimals.

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Problem 97

Find the range for at least $75\%$ of Americans' online time using Chebyshev's theorem, with an average of 4 hours and SD of 27 min.

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Problem 98

Find the range for online time where at least 75% of Americans lie, using Chebyshev's theorem. Average: 4 hrs, SD: 27 min.

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Problem 99

Find the range, variance, and standard deviation for the data set: 23, 32, 31, 45, 25, 33, 44, 47, 37, 32, 37, 48, 47, 50, 22, 40, 30, 28, 22, 39. Range is 28. Use sample formulas.

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Problem 100

Find the range, variance, and standard deviation of the data set: 23, 32, 31, 45, 25, 33, 44, 47, 37, 32, 37, 48, 47, 50, 22, 40, 30, 28, 22, 39. Use sample formulas.

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Measures of Spread

Problem 1

Find the z z z-score for x=7 x=7 x=7 given a random variable X X X with mean 4 and standard deviation 2.

Problem 2

Find the z z z-score for x=7 x = 7 x=7 given that the mean μ=4 \mu = 4 μ=4 and standard deviation σ=2 \sigma = 2 σ=2.

Problem 3

Um zootecnista testa nova ração para coelhos. Qual média deve ser superior para trocar a ração atual? (A) 5,0 (B) 9,5 (C) 10,0 (D) 10,5 (E) 15,0.

Problem 4

Find scores at 1, 2, and 3 standard deviations above the mean for: a. μ=13.2\mu=13.2μ=13.2, σ=4.2\sigma=4.2σ=4.2; b. μ=86.1\mu=86.1μ=86.1, σ=12.5\sigma=12.5σ=12.5; c. μ=521.4\mu=521.4μ=521.4, σ=81.7\sigma=81.7σ=81.7.

Problem 5

Problem 6

Is a 24.7-second 100-m dash satisfactory if last year's average was μ=28.5\mu=28.5μ=28.5 and σ=3.1\sigma=3.1σ=3.1? Explain.

Problem 7

Find the mean and standard deviation for these data sets: a. Set AAA: below 12.3, above 17.8. b. Set BBB: below 3.51, above 41.16. c. Set CCC: below 12.41, above 35.12.

Problem 8

Problem 9

Describe a distribution that is NOT normally distributed.

Problem 10

Find the scores at 1, 2, and 3 standard deviations above the mean for: a. μ=13.2\mu=13.2μ=13.2, σ=4.2\sigma=4.2σ=4.2; b. μ=86.1\mu=86.1μ=86.1, σ=12.5\sigma=12.5σ=12.5; c. μ=521.4\mu=521.4μ=521.4, σ=81.7\sigma=81.7σ=81.7.

Problem 11

Calculate the inflation rate from 2015 to 2016 using CPI: Inflation Rate=CPI2016−CPI2015CPI2015×100 \text{Inflation Rate} = \frac{CPI_{2016} - CPI_{2015}}{CPI_{2015}} \times 100 Inflation Rate=CPI2015​CPI2016​−CPI2015​​×100

Problem 12

Mike wants to evaluate Hi-Tech Inc. stock. Calculate annual returns from 2009 to 2012, find standard deviation, and determine if the coefficient of variation is below 0.90 for investment.

Problem 13

Problem 14

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return rpr_{p}rp​, b) average return rˉp\bar{r}_{p}rˉp​, c) standard deviation σrp\sigma_{r_{p}}σrp​​, d) correlation of returns, e) diversification benefits.

Problem 15

Find the relative error of a car's speed measured as 48 km/h48 \mathrm{~km} / \mathrm{h}48 km/h, rounded to the nearest km/h\mathrm{km} / \mathrm{h}km/h.

Problem 16

A jogging track is 500 m500 \mathrm{~m}500 m long with a 0.1%0.1 \%0.1% error. What is the scale interval of the measuring tool?

Problem 17

Find the max absolute error, measured time, and percentage error for ttt with 25.465≤t<25.47525.465 \leq t < 25.47525.465≤t<25.475.

Problem 18

Find the percentage error in measuring an elephant's weight, capped at 5825 kg5825 \mathrm{~kg}5825 kg, with a 10 kg10 \mathrm{~kg}10 kg scale.

Problem 19

Problem 20

Find how many standard deviations each score xxx is from the mean μ\muμ for the given distributions.

Problem 21

Find the ZZZ-score for these Math test scores: mean = 36, standard deviation = 8. Scores: 26, 39, 42, 32, 37.

Problem 22

Find the ZZZ-score for a student who scored 74 on a test with an average of 80 and a standard deviation of 6.

Problem 23

Determine if a 100-m dash time of 24.7 seconds is satisfactory given μ=28.5\mu=28.5μ=28.5 and σ=3.1\sigma=3.1σ=3.1.

Problem 24

Problem 25

Find Patrick's ZZZ-score if he scored 85 on a test with a mean of 100 and a standard deviation of 15.

Problem 26

Evaluate investments X, Y, Z against a return of 12%12\%12% and 6%6\%6% SD. Choose based on risk preferences: neutral, averse, seeking.

Problem 27

Sharon Smith evaluates investments X, Y, Z against a 12% return and 6% risk. Determine selections for risk neutral, averse, and seeking.

Problem 28

Find the z\mathrm{z}z-score for x=7\mathrm{x}=7x=7 given that the mean of X\mathrm{X}X is 4 and the standard deviation is 2.

Problem 29

Find the z\mathrm{z}z-score for x=7\mathrm{x}=7x=7 given that the mean of X\mathrm{X}X is 4 and standard deviation is 2.

Problem 30

Find the skewness (=4.217=4.217=4.217) and kurtosis (=18.342=18.342=18.342) of the data and describe the distribution shape.

Problem 31

Find the class width if the range is 71.4, measurement unit is 0.001, and there are 10 classes.

Problem 32

A pencil measures 7.50 cm7.50 \, \text{cm}7.50cm. Find (a) max absolute error, (b) relative error, (c) percentage error. Use 3 sig. figs.

Problem 33

Calculate the average return, covariance, and correlation coefficient for Merias and Gangnam based on their monthly returns.

Problem 34

Find a 99%99\%99% confidence interval for the standard deviation σ\sigmaσ of washing machine replacement times from a sample of 20, with mean 11.6 and SD 2.2. Calculate χL2\chi_{L}^{2}χL2​, χR2\chi_{R}^{2}χR2​, and interpret the interval.

Problem 35

For males, systolic blood pressure is normal with mean 120 and SD 5. Find the interval for the middle 68%68\%68%.

Problem 36

Find the systolic blood pressure range for the middle 99.7%99.7\%99.7% of males, given a mean of 105 and SD of 10.

Problem 37

Find the z-score for a person who scored 26 on an exam with a mean of 24 and a standard deviation of 4.

Problem 38

Find the systolic blood pressure range for the middle 99.7%99.7\%99.7% of males, given mean 125125125 and SD 777.

Problem 39

Find the z-score for a person who scored 128 on a test with a mean of 100 and a standard deviation of 10: z=128−10010z = \frac{128 - 100}{10}z=10128−100​.

Problem 40

Find the z-score for a score of 47 on a test with a mean of 36 and standard deviation of 4. Use z=x−μσz = \frac{x - \mu}{\sigma}z=σx−μ​.

Problem 41

Find the z-score for a score of 160 on a standardized exam where the mean is 135 and the standard deviation is 25.

Problem 42

Find the z-score for a score of 350 on a normal distribution with mean 300 and standard deviation 40.

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

Find scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

Find the mean and standard deviation for these data sets: a. Set $A$ : below 12.3, above 17.8. b. Set $B$ : below 3.51, above 41.16. c. Set $C$ : below 12.41, above 35.12.

Find the scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

Calculate the inflation rate from 2015 to 2016 using CPI: $\text{Inflation Rate} = \frac{CPI_{2016} - CPI_{2015}}{CPI_{2015}} \times 100$

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return $r_{p}$ , b) average return $\bar{r}_{p}$ , c) standard deviation $\sigma_{r_{p}}$ , d) correlation of returns, e) diversification benefits.

Find the relative error of a car's speed measured as $48 \mathrm{~km} / \mathrm{h}$ , rounded to the nearest $\mathrm{km} / \mathrm{h}$ .

A jogging track is $500 \mathrm{~m}$ long with a $0.1 \%$ error. What is the scale interval of the measuring tool?

Find the max absolute error, measured time, and percentage error for $t$ with $25.465 \leq t < 25.475$ .

Find the percentage error in measuring an elephant's weight, capped at $5825 \mathrm{~kg}$ , with a $10 \mathrm{~kg}$ scale.

Find how many standard deviations each score $x$ is from the mean $\mu$ for the given distributions.

Find the $Z$ -score for these Math test scores: mean = 36, standard deviation = 8. Scores: 26, 39, 42, 32, 37.

Find the $Z$ -score for a student who scored 74 on a test with an average of 80 and a standard deviation of 6.

Determine if a 100-m dash time of 24.7 seconds is satisfactory given $\mu=28.5$ and $\sigma=3.1$ .

Find Patrick's $Z$ -score if he scored 85 on a test with a mean of 100 and a standard deviation of 15.

Evaluate investments X, Y, Z against a return of $12\%$ and $6\%$ SD. Choose based on risk preferences: neutral, averse, seeking.

Find the $\mathrm{z}$ -score for $\mathrm{x}=7$ given that the mean of $\mathrm{X}$ is 4 and the standard deviation is 2.

Find the $\mathrm{z}$ -score for $\mathrm{x}=7$ given that the mean of $\mathrm{X}$ is 4 and standard deviation is 2.

Find the skewness ( $=4.217$ ) and kurtosis ( $=18.342$ ) of the data and describe the distribution shape.

A pencil measures $7.50 \, \text{cm}$ . Find (a) max absolute error, (b) relative error, (c) percentage error. Use 3 sig. figs.

Find a $99\%$ confidence interval for the standard deviation $\sigma$ of washing machine replacement times from a sample of 20, with mean 11.6 and SD 2.2. Calculate $\chi_{L}^{2}$ , $\chi_{R}^{2}$ , and interpret the interval.

For males, systolic blood pressure is normal with mean 120 and SD 5. Find the interval for the middle $68\%$ .

Find the systolic blood pressure range for the middle $99.7\%$ of males, given a mean of 105 and SD of 10.

Find the systolic blood pressure range for the middle $99.7\%$ of males, given mean $125$ and SD $7$ .

Find the z-score for a person who scored 128 on a test with a mean of 100 and a standard deviation of 10: $z = \frac{128 - 100}{10}$ .

Find the z-score for a score of 47 on a test with a mean of 36 and standard deviation of 4. Use $z = \frac{x - \mu}{\sigma}$ .

Find the z-score for a score of 210, given a mean of 200 and a standard deviation of 20. Use $z = \frac{x - \mu}{\sigma}$ .

Find the standard deviation of human pregnancy lengths given a mean of 267 days and $95\%$ lasting between 245 and 289 days. What percent last at least 285 days? Standard deviation: $\square$ days.

Find the cutoff score for an $A$ if the mean is 74 and the standard deviation is 8.11, top $6\%$ .

Calculate the expected return $r_{p}$ for a portfolio of stocks L (40\%) and M (60\%) over 2013-2018, then find $\bar{r}_{p}$ and $\sigma_{r_{p}}$ . Discuss correlation and diversification benefits.

Survey shows $56\%$ in favor and $44\%$ opposed to a garage sale. Find least and greatest percent opposed ( $\pm 5\%$ ). Is half the town opposed? Explain.

Find the interquartile range of the data set: $10, 3, 7, 6, 9, 12, 13$ .