A researcher takes 10 samples of 20 students each to get a sampling distribution of the average number of siblings students at a university have. According to the Central Limit Theorem, what can the researcher do make their sampling distribution get closer to normal?

Finding Probabilities for Sampling Distributions In Exercises 29–32, find the indicated probability and interpret the results.

Dow Jones Industrial Average From 1975 through 2020, the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 32 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 700? Assume sigma=1540

Finding Probabilities for Sampling Distributions In Exercises 29–32, find the indicated probability and interpret the results.

Asthma Prevalence by State The mean percent of asthma prevalence of the 50 U.S. states is 9.51%. A random sample of 30 states is selected. What is the probability that the mean percent of asthma prevalence for the sample is greater than 10%? Assume sigma=1.17%

Which Is More Likely? Assume that the fertility rates in Exercise 32 are normally distributed. Are you more likely to randomly select a state with a fertility rate of less than 65 or to randomly select a sample of 15 states in which the mean of the state fertility rates is less than 65? Explain.

For a new advertising campaign, a video game retailer is interested in including information on the average play time of their most popular game. They get 100 random samples of 40 players and obtain their play time to get a sampling distribution. The mean of the sampling distribution is 26.7 hours. In this example, what is the value of $n$?

A company’s marketing team takes 50 samples of 10 recent clients to create a sampling distribution of sample means for the average amount spent per month on company products. Can the Central Limit Theorem be used to determine that the sampling distribution is normal?

If ${\mu }_X=3.2$ and ${\sigma }_X=0.98$, find the probability of getting a sample mean above 3.5 in a sample of 60 people.

In Exercises 39 and 40, determine whether the finite correction factor should be used. If so, use it in your calculations when you find the probability.

Old Faithful In a sample of 100 eruptions of the Old Faithful geyser at Yellowstone National Park, the mean interval between eruptions was 129.58 minutes and the standard deviation was 108.54 minutes. A random sample of size 30 is selected from this population. What is the probability that the mean interval between eruptions is between 120 minutes and 140 minutes?

Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.

Renewable Energy The zloty is the official currency of Poland. During a recent period of two years, the day-ahead prices for renewable energy in Poland (in zlotys per mega-watt hour) have a mean of 158.51 and a standard deviation of 33.424. Random samples of size 100 are drawn from this population, and the mean of each sample is determined. (Adapted from Multidisciplinary Digital Publishing Institute)