Distribution

Problem 1

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

See Solution

Problem 2

Calculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

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Problem 3

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

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Problem 4

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

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Problem 5

Identify which statements are true or false regarding confidence intervals and distributions.

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Problem 6

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula $E[X]$ y $\operatorname{Var}[X]$ .

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Problem 7

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 8

A company has 125 employees with the following absence probabilities: $0$ days (0.60), $1$ day (0.20), $2$ days (0.12), $3$ days (0.04), $4$ days (0.04), $5$ days (0.00). Find the mean days absent.

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Problem 9

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

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Problem 10

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 11

Find the probability that a computer has an internet speed > 8.7 Mbps, given mean = 5.5 Mbps, SD = $1.6 \mathrm{Mbps}$ .

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Problem 12

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 13

Find the percentage of aloe vera plants with heights between $8.0 \mathrm{~cm}$ and $13.2 \mathrm{~cm}$ , given average $10.6 \mathrm{~cm}$ and SD $1.3 \mathrm{~cm}$ .

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Problem 14

Find the percentage of blood samples with coagulation time > 16.5 minutes, given mean = 10 min, SD = 6.5 min.

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Problem 15

A scientist tests guava's effectiveness in filtering waste water. What is the probability that it absorbs more than $80 \mathrm{ppm}$ ?

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Problem 16

Find the probability that more than $0.03 \mathrm{~g}$ of steel is lost, given an average loss of $0.06 \mathrm{~g}$ and a standard deviation of $0.015 \mathrm{~g}$ .

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Problem 17

Describe a distribution that is NOT normally distributed.

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Problem 18

Find missing frequencies f1 and f2 for the intervals 0-20, 20-40, 40-60, 60-80, 80-100, 100-120 with mean 57.6 and sum 50.

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Problem 19

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

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Problem 20

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 21

Find the probability that a computer's internet speed exceeds 8.7 Mbps, given an average of 5.5 Mbps and a standard deviation of $1.6 \mathrm{Mbps}$ .

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Problem 22

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

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Problem 23

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 24

Find probabilities for lemonade consumption: more than 21 gallons, less than 19 gallons, and between 20-25 gallons. Also, find sodium probabilities for dinners and construct a confidence interval for garlic's effect on cholesterol.

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Problem 25

Find probabilities for lemonade consumption: a) > 21 gallons, b) < 19 gallons, c) between 20 and 25 gallons. For sodium: a) > 670 mg in one dinner, c) mean > 670 mg in 10 dinners. Also, estimate the mean LDL cholesterol change from garlic treatment.

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Problem 26

3.- Identity theft and probabilities: a) Find the chance of randomly getting your 9-digit social security number. b) If someone knows the last 4 digits, what's the chance the other digits match yours?
4.- Binomial Distribution: For a 25% belief in death penalty reducing homicides among 8 police chiefs, find: a) Probability exactly 5 believe this. b) Probability at least 2 believe this.
Also, for a class of 75 with a 12% absentee rate, find the mean, variance, and standard deviation of absentees.

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Problem 27

1. Find the probability of randomly generating a 9-digit SSN that matches yours and if the last 4 digits are known.
2. In a sample of 8 police chiefs, find the probability that exactly 5 believe the death penalty reduces homicides and at least 2 do.
3. For a class of 75 with a 12% absentee rate, calculate the mean, variance, and standard deviation of absent students.

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Problem 28

1. For a football team with mean 20 gallons and SD 3, find probabilities for: a) >21, b) <19, c) between 20-25 gallons.
2. For a low-salt dinner with mean 660 mg sodium and SD 35 mg, find probabilities for: a) >670 mg, c) sample mean >670 mg for 10 dinners.
3. For garlic treatment on 47 subjects, mean LDL change is 3.2 and SD is 18.6. What is the best point estimate of the mean?

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Problem 29

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

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Problem 30

Find the median speed of 510 vehicles with mean $99 \mathrm{~km/h}$ and std dev $9 \mathrm{~km/h}$ . What % travel < $117 \mathrm{~km/h}$ ?

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Problem 31

Binomial Distribution: For 8 police chiefs with a $25\%$ belief in the death penalty's effect, find: a. P(exactly 5 believe) b. P(at least 2 believe)
Also, for a class of 75 with a $12\%$ absentee rate, find mean, variance, and standard deviation of absentees.

See Solution

Problem 32

求车程时间 $T$ 的分布列与期望 $E(T)$ ，并计算刘教授往返时间不超120分钟的概率。

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Problem 33

1.- Given mean blood pressure is 120 mmHg and SD is 5.6. Find z-scores and sketch normal curves. a. Find P(120 < X < 121.8) b. Find P(120 < \bar{X} < 121.8) for a sample of 30.

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Problem 34

A postal carrier delivered letters, ads, and magazines. Find probabilities for various scenarios based on the total distributions.

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Problem 35

Find the percentile of 7.1 lbs, calculate $Q_{1}, Q_{2}, Q_{3}$ , create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

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Problem 36

4.- Binomial Distribution. Last year, $64\%$ of adults liked superhero movies. For 7 adults, find: a) Probability exactly 4 enjoy them. b) Probability at least 6 enjoy them.

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Problem 37

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 38

7.- A pro shop has a probability distribution for golf ball orders. a) Find the probability of ordering at most 2 golf balls. b) Find the probability of ordering at least one golf ball. c) Find the mean.
8.- A teacher claims the mean height of 5-year-olds is more than 95 cm. a) State the null and alternative hypothesis. b) Find the test statistic. c) Find the P-value or critical points. d) Make a decision using P-value or critical values. e) State your conclusion.

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Problem 39

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 40

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 41

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 42

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

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Problem 43

Find the $z$ -score for a person who scored 616 on an exam with mean 500 and standard deviation 40.

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Problem 44

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 45

Find the mode, median, and mean of the weekly wages of 65 employees: 55 (8), 65 (10), 785 (16), 85 (14), 95 (10), 105 (5), 115 (2).

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Problem 46

Un'urna ha 2 palline bianche e 3 nere. Calcola la probabilità di estrazione della pallina bianca in 7 tentativi: a. solo la prima volta; b. una volta; c. 5 volte; d. sempre; e. mai; f. almeno una volta.

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Problem 47

Find the mode and median of the ages of 21 students: 16 (6), 17 (3), 18 (8), 19 (4) years.

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Problem 48

Complete the frequency table and find the mean, given $\Sigma f = 113$ and $\Sigma f x = 292$ .

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Problem 49

Complete the frequency table, calculate the mean ( $\frac{292}{113} \approx 2.6$ ), and find the median.

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Problem 50

Calculate the estimated mean revision time for 120 students given the following time intervals and frequencies:
$0<t \leq 15$ : 0, $15<t \leq 30$ : 20, $30<t \leq 45$ : 50, $45<t \leq 60$ : 50.

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Problem 51

(a) Fill in the missing values in the frequency distribution table. (b) Find the mean: $\frac{292}{113} \approx 2.6$ . (c) Determine the median. (d) Create a frequency histogram.

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Problem 52

A, B, and C invest in the ratio $\frac{2}{3} : \frac{3}{5} : \frac{5}{6}$ . A adds 25\% after 8 months. Profit is 5820. Find C's share.

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Problem 53

Find the central tendency measures (mode, median, mean) and compute range, IQR, quartile deviation, and standard deviation for the data: Marks: 0-20 (5), 20-40 (15), 40-60 (30), 60-80 (8), 80-100 (2).

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Problem 54

Find the probability that the battery lasts between 50 and 70 hours for a computer with mean 50 and SD 15 hours.

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Problem 55

Explain how the Distributive Property aids in solving problems.

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Problem 56

Conjecture the percentage of the population with type O blood from a sample result of 0.42. Is it descriptive or inferential statistics?

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Problem 57

Find the modal class of wallaby heights and estimate the mean and standard deviation from the data given.

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Problem 58

Al surveyed 60 people on restaurant spending.
a) Identify the modal class.
b) Estimate the mean.
c) Estimate the standard deviation and discuss it.
d) Estimate the variance, range, and interquartile range, explaining why they are estimates.

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Problem 59

Dibuja un histograma de los tiempos de pago: $19,15,43,39,35,31,27,22,18,14,42,38,13,13,13,41,41,41,37,37,37,33$ . Usa límites de clase 12.5 y ancho 7.

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Problem 60

Find the grouped frequency distribution for these test scores: 83, 85, 97, 91, 92, 82, 90, 89, 91, 83, 93, 88, 86, 84, 98. Class width is 5. Then, draw a frequency polygon with midpoints labeled.

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Problem 61

Analyze the frequency table of art styles to determine if there's an association between art type and style.

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Problem 62

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

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Problem 63

Micro-Pub, Inc. is evaluating two cameras (R and S).
a. Find the rate of return range for both cameras. b. Calculate the expected return for each camera. c. Which camera is riskier and why?
Initial investment: \$4,000 for both. Camera R: Pessimistic 20%, Most likely 25% (0.50), Optimistic 30% (0.25). Camera S: Pessimistic 15% (0.20), Most likely 25% (0.55), Optimistic 35% (0.25).

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Problem 64

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 65

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 66

Find the standard deviation of human pregnancy lengths given a mean of 267 days and a range of 245 to 289 days. What percent last at least 285 days?

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Problem 67

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 68

Normal distribution: Given expected return $\bar{r} = 18.9\%$ and $C V = 0.75$ , find: a. $\sigma_{r}$ , b. ranges for $68\%, 95\%, 99\%$ , c. draw the distribution.

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Problem 69

Identify the probability method the farmer used to find a $32\%$ chance of milking between 12 and 14 gallons.

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Problem 70

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 71

Create a stem-and-leaf plot using the scores: 50, 57, 51, 69, 66, 94, 73, 77, 59, 64, 50, 57, 71, 85, 59, 72, 56, 85, 64, 53, 62, 83, 70, 73, 68, 95, 85, 60, 52. Describe the distribution shape.

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Problem 72

Count the cola preferences from the data: Shasta, Coke, and Pepsi. Create a frequency and relative frequency table.

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Problem 73

Create a stem-and-leaf plot for these scores: 55, 59, 69, 50, 76, 74, 62, 85, 69, 89, 69, 54, 51, 56, 95, 60, 55, 76, 77, 69, 80, 70, 53, 59, 57, 63, 63, 53, 73. Describe its shape.

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Problem 74

Given the frequency distribution, find the mean, median, and mode of the data set. Round to two decimal places.

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Problem 75

Approximate the mean for the given frequency distribution:
Class: $50-54$ (1), $55-59$ (3), $60-64$ (8), $65-69$ (14), $70-74$ (17), $75-79$ (15), $80-84$ (7), $85-89$ (4), $90-94$ (1).
Round to one decimal place.

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Problem 76

Find the lower class limits, upper class limits, class width, midpoints, boundaries, and total individuals for:
Age (yr) Frequency 20-29: 27, 30-39: 33, 40-49: 15, 50-59: 4, 60-69: 5, 70-79: 2, 80-89: 2.

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Problem 77

Find the lower class limits, upper class limits, class width, midpoints, boundaries, and total individuals for the data.

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Problem 78

Given a stem-and-leaf plot, find the mean, median, standard deviation, range, and data shape (right, left, symmetric).

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Problem 79

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 80

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 81

Is the frequency distribution normal based on the criteria? Choose A, B, or C based on the given temperature ranges and frequencies.

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Problem 82

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 83

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 84

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

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Problem 85

In football, if 425 players are drafted, how many will have IQs within one standard deviation of the mean (100, $\sigma = 15$ )?

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Problem 86

At a university, $50\%$ of students play intramural volleyball. What is the probability a randomly chosen student participates?

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Problem 87

A light bulb lasts $N(1100, 60)$ hours. If 3/5 of bulbs are used, how many last between 1050 and 1140 hours?

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Problem 88

Find the expected number of light bulbs lasting between 1050 and 1140 hours from 375 bulbs, given mean = 1100, SD = 60.

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Problem 89

What is the probability that less than 2 of your 5 siblings will visit you, given probabilities for 0 to 5 visitors?

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Problem 90

In a college, 70% of classes are taught by adjuncts. What's the chance a student taking 5 classes has no adjunct professors?

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Problem 91

Find the expression for the probability of 240 cars parked in Lot A, given the mean is 200. Options include: a. $\mathrm{e}^{240} / 200$ ! b. $240 ! / 200$ ! c. $\mathrm{e}^{-200} 200^{240} / 240$ ! d. $e^{-240} 240^{200} / 200$ !

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Problem 92

What is the probability of getting a number between 0.57 and 0.85 from a uniform distribution between 0 and 1? a. $15 \%$ b. $28 \%$ c. $32 \%$ d. $57 \%$

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Problem 93

Find the percentile rank for an IQ score of 100 using the standard normal distribution (z-distribution).

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Problem 94

Find the percentile for a score of 156 given a mean of 120 and a standard deviation of 12.

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Problem 95

Find the proportion of scores in a $z$ distribution between $z = -1.00$ and $z = 1.00$ . Options: .2500, .6826, .3413, .5000.

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Problem 96

Find the proportion of scores in a $\mathrm{z}$ distribution between $\mathrm{z} = -2.00$ and $\mathrm{z} = 0.00$ .

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Problem 97

Find the proportion of scores in a $z$ distribution between $z = 0.00$ and $z = 2.00$ . Options: .3413, .4772, .7500, .8176.

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Problem 98

Find the proportion of SAT verbal scores between 400 and 600, given a mean of 500 and a standard deviation of 100.

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Problem 99

Find the proportion of SAT verbal scores between 200 and $800$ using the $z$ distribution. Choices: .3413, .2500, .5000, .9970.

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Problem 100

Find the z score that separates the lower 50% of the z distribution: 0.00, 1.96, $-1.00$ , or $-1.96$ ?

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Distribution

Problem 1

Find the z z z-score for x=7 x=7 x=7 given that the mean is 4 and the standard deviation is 2.

Problem 2

Calculate the expected value of winnings with payouts 2,3,4,5,62, 3, 4, 5, 62,3,4,5,6 and probabilities 0.40,0.20,0.17,0.13,0.100.40, 0.20, 0.17, 0.13, 0.100.40,0.20,0.17,0.13,0.10. Round to the nearest hundredth.

Problem 3

True or false: For a population proportion confidence interval, we use z\mathrm{z}z-distribution, not t\mathrm{t}t-distribution.

Problem 4

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known σ\sigmaσ and Z, 4) unknown σ\sigmaσ and S, 5) t vs z for population proportion.

Problem 5

Identify which statements are true or false regarding confidence intervals and distributions.

Problem 6

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula E[X]E[X]E[X] y Var⁡[X]\operatorname{Var}[X]Var[X].

Problem 7

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 8

A company has 125 employees with the following absence probabilities: 000 days (0.60), 111 day (0.20), 222 days (0.12), 333 days (0.04), 444 days (0.04), 555 days (0.00). Find the mean days absent.

Problem 9

Find the probability density function of a normal distribution with mean 1 and standard deviation 12\frac{1}{2}21​.

Problem 10

Problem 11

Find the probability that a computer has an internet speed > 8.7 Mbps, given mean = 5.5 Mbps, SD = 1.6Mbps1.6 \mathrm{Mbps}1.6Mbps.

Problem 12

Problem 13

Find the percentage of aloe vera plants with heights between 8.0 cm8.0 \mathrm{~cm}8.0 cm and 13.2 cm13.2 \mathrm{~cm}13.2 cm, given average 10.6 cm10.6 \mathrm{~cm}10.6 cm and SD 1.3 cm1.3 \mathrm{~cm}1.3 cm.

Problem 14

Find the percentage of blood samples with coagulation time > 16.5 minutes, given mean = 10 min, SD = 6.5 min.

Problem 15

A scientist tests guava's effectiveness in filtering waste water. What is the probability that it absorbs more than 80ppm80 \mathrm{ppm}80ppm?

Problem 16

Find the probability that more than 0.03 g0.03 \mathrm{~g}0.03 g of steel is lost, given an average loss of 0.06 g0.06 \mathrm{~g}0.06 g and a standard deviation of 0.015 g0.015 \mathrm{~g}0.015 g.

Problem 17

Describe a distribution that is NOT normally distributed.

Problem 18

Find missing frequencies f1 and f2 for the intervals 0-20, 20-40, 40-60, 60-80, 80-100, 100-120 with mean 57.6 and sum 50.

Problem 19

Find the probability density function of a normal distribution with mean 1 and standard deviation 12\frac{1}{2}21​.

Problem 20

Problem 21

Find the probability that a computer's internet speed exceeds 8.7 Mbps, given an average of 5.5 Mbps and a standard deviation of 1.6Mbps1.6 \mathrm{Mbps}1.6Mbps.

Problem 22

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

Problem 23

Problem 24

Find probabilities for lemonade consumption: more than 21 gallons, less than 19 gallons, and between 20-25 gallons. Also, find sodium probabilities for dinners and construct a confidence interval for garlic's effect on cholesterol.

Problem 25

Find probabilities for lemonade consumption: a) > 21 gallons, b) < 19 gallons, c) between 20 and 25 gallons. For sodium: a) > 670 mg in one dinner, c) mean > 670 mg in 10 dinners. Also, estimate the mean LDL cholesterol change from garlic treatment.

Problem 26

Problem 27

Problem 28

Problem 29

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 30

Find the median speed of 510 vehicles with mean 99 km/h99 \mathrm{~km/h}99 km/h and std dev 9 km/h9 \mathrm{~km/h}9 km/h. What % travel < 117 km/h117 \mathrm{~km/h}117 km/h?

Problem 31

Binomial Distribution: For 8 police chiefs with a 25%25\%25% belief in the death penalty's effect, find: a. P(exactly 5 believe) b. P(at least 2 believe)Also, for a class of 75 with a 12%12\%12% absentee rate, find mean, variance, and standard deviation of absentees.

Problem 32

求车程时间 TTT 的分布列与期望 E(T)E(T)E(T)，并计算刘教授往返时间不超120分钟的概率。

Problem 33

1.- Given mean blood pressure is 120 mmHg and SD is 5.6. Find z-scores and sketch normal curves. a. Find P(120 < X < 121.8) b. Find P(120 < \bar{X} < 121.8) for a sample of 30.

Problem 34

A postal carrier delivered letters, ads, and magazines. Find probabilities for various scenarios based on the total distributions.

Problem 35

Find the percentile of 7.1 lbs, calculate Q1,Q2,Q3Q_{1}, Q_{2}, Q_{3}Q1​,Q2​,Q3​, create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

Problem 36

4.- Binomial Distribution. Last year, 64%64\%64% of adults liked superhero movies. For 7 adults, find: a) Probability exactly 4 enjoy them. b) Probability at least 6 enjoy them.

Problem 37

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 38

Problem 39

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

Problem 40

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 41

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 42

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

Problem 43

Find the zzz-score for a person who scored 616 on an exam with mean 500 and standard deviation 40.

Problem 44

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

Calculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula $E[X]$ y $\operatorname{Var}[X]$ .

A company has 125 employees with the following absence probabilities: $0$ days (0.60), $1$ day (0.20), $2$ days (0.12), $3$ days (0.04), $4$ days (0.04), $5$ days (0.00). Find the mean days absent.

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

Find the probability that a computer has an internet speed > 8.7 Mbps, given mean = 5.5 Mbps, SD = $1.6 \mathrm{Mbps}$ .

Find the percentage of aloe vera plants with heights between $8.0 \mathrm{~cm}$ and $13.2 \mathrm{~cm}$ , given average $10.6 \mathrm{~cm}$ and SD $1.3 \mathrm{~cm}$ .

A scientist tests guava's effectiveness in filtering waste water. What is the probability that it absorbs more than $80 \mathrm{ppm}$ ?

Find the probability that more than $0.03 \mathrm{~g}$ of steel is lost, given an average loss of $0.06 \mathrm{~g}$ and a standard deviation of $0.015 \mathrm{~g}$ .

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

Find the probability that a computer's internet speed exceeds 8.7 Mbps, given an average of 5.5 Mbps and a standard deviation of $1.6 \mathrm{Mbps}$ .

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

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

Find the median speed of 510 vehicles with mean $99 \mathrm{~km/h}$ and std dev $9 \mathrm{~km/h}$ . What % travel < $117 \mathrm{~km/h}$ ?

Binomial Distribution: For 8 police chiefs with a $25\%$ belief in the death penalty's effect, find: a. P(exactly 5 believe) b. P(at least 2 believe)
Also, for a class of 75 with a $12\%$ absentee rate, find mean, variance, and standard deviation of absentees.

求车程时间 $T$ 的分布列与期望 $E(T)$ ，并计算刘教授往返时间不超120分钟的概率。

Find the percentile of 7.1 lbs, calculate $Q_{1}, Q_{2}, Q_{3}$ , create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

4.- Binomial Distribution. Last year, $64\%$ of adults liked superhero movies. For 7 adults, find: a) Probability exactly 4 enjoy them. b) Probability at least 6 enjoy them.

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 616 on an exam with mean 500 and standard deviation 40.

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

Complete the frequency table and find the mean, given $\Sigma f = 113$ and $\Sigma f x = 292$ .

Complete the frequency table, calculate the mean ( $\frac{292}{113} \approx 2.6$ ), and find the median.

Calculate the estimated mean revision time for 120 students given the following time intervals and frequencies:
$0<t \leq 15$ : 0, $15<t \leq 30$ : 20, $30<t \leq 45$ : 50, $45<t \leq 60$ : 50.

(a) Fill in the missing values in the frequency distribution table. (b) Find the mean: $\frac{292}{113} \approx 2.6$ . (c) Determine the median. (d) Create a frequency histogram.

A, B, and C invest in the ratio $\frac{2}{3} : \frac{3}{5} : \frac{5}{6}$ . A adds 25\% after 8 months. Profit is 5820. Find C's share.

Al surveyed 60 people on restaurant spending.
a) Identify the modal class.
b) Estimate the mean.
c) Estimate the standard deviation and discuss it.
d) Estimate the variance, range, and interquartile range, explaining why they are estimates.

Dibuja un histograma de los tiempos de pago: $19,15,43,39,35,31,27,22,18,14,42,38,13,13,13,41,41,41,37,37,37,33$ . Usa límites de clase 12.5 y ancho 7.

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 $6\%$ .

Normal distribution: Given expected return $\bar{r} = 18.9\%$ and $C V = 0.75$ , find: a. $\sigma_{r}$ , b. ranges for $68\%, 95\%, 99\%$ , c. draw the distribution.

Identify the probability method the farmer used to find a $32\%$ chance of milking between 12 and 14 gallons.