## MATH 399N Week 5 MyStatLab Homework Solutions: Section 5.2, 5.3, 5.4

**1. Question: 5.2.7-T **In a survey of a group of men, the heights in the 20-29 age group were normally …, with a mean of 69.8 inches and a standard deviation of 2.0 inches. A study participant is randomly … Complete parts (a) through (d) below.

**2. Question: 5.2.1 **Assume the random variable x is normally distributed with mean μ = 87 and standard deviation σ = 4. Find the indicated probability.

P(x < 80)

**3. Question: 5.2.8 **The amounts a soft drink machine is designed to dispense for each drink are normally …, with a mean of 12.3 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly …

- Find the probability that the drink is less than 12.1 fluid ounces.
- ……………………. between 11.9 and 12.1 fluid ounces.
- Find the probability that the drink is more than 12.6 fluid ounces. Can this … an unusual event? Explain your reasoning

**4. Question: 5.3.33 **The time spent (in days) waiting for a heart transplant for people ages 35-49 can … approximated by the normal distribution, as shown in the figure to the right,

- What waiting time represents the 5
^{th}percentile? - What waiting time represents the third quartile?

**5. Question: 5.3.34 **The time spent (in days) waiting for a kidney transplant for people ages 35-49 can … approximated by the normal distribution, as shown in the figure to the right.

- What waiting time represents the 99
^{th}percentile? - What waiting time represents the first quartile?

**6. Question: 5.4.1 **A population has a mean μ = 85 and a standard deviation σ = 6. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 36.

**7. Question: 5.4.9 **The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 225 is drawn from the population. Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning.

## STATUS

**8. Question: 5.4.27-T **Find the probability and interpret the results. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialists is about $60,000. A random sample of 31 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57500? Assume σ = $6200.

**9. Question: 5.4.31 **The mean height of women in a country (ages 20 – 29) is 63.8 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ = 2.51

**10. Question: 5.4.35 **A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 139 ounces and a standard deviation of 0.40 ounces. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 138.9 ounces. Does the machine need to … reset? Explain your reasoning.

**11. Question: 5.4.38 **A manufacturer claims that the life span of its tires is 52000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally … You select 100 tires at random and test them. The mean life span is 51729 miles. Assume σ = 900. Complete parts (a) through(c).