Exam 10: Sampling Distributions

In a given year, the average annual salary of an Rugby player was $205 000, with a standard deviation of $24 500. If a simple random sample of 50 players is taken, what is the probability that the sample mean will be less than $210 000?

A manufacturing company is concerned about the number of defective items produced by their assembly line. In the past they have had 5% of their products produced defectively. They take a random sample of 35 products. What is the probability that more than 5 products in the sample are defective? A. 14.28\% B. 0.59\% C. 100\% D. None of these choices are correct

A video rental store wants to know what proportion of its customers are under 21 years old. A simple random sample of 500 customers is taken, and 350 of them are under 21. Assume that the true population proportion of customers aged under 21 is 0.68. Describe the sampling distribution of proportion of customers who are under age 21.

A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is: A. 0.0166. B. 0.0228. C. 0.3708 D. 0.0394.

The standard deviation of a sampled population is also called the standard error of the sample mean.

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is called the: \begin{array}{|l|l|}\hline A&\text {standard error of \bar{X} . }\\\hline B&\text {expected value of \( \bar{X} \). }\\\hline C&\text {sampling distribution of \( \bar{X} \). }\\\hline D&\text {normal distribution. }\\\hline \end{array}

A video rental store wants to know what proportion of its customers are under 21 years old. A simple random sample of 500 customers is taken, and 375 of them are under 21. Assume that the true population proportion of customers aged under 21 is 0.68. What is the probability that the sample proportion will be within 0.03 of the true proportion of customers who are aged under 21?

The heights of 9-year-old children are normally distributed, with a mean of 123 cm and a standard deviation of 10 cm. a. Find the probability that one randomly selected 9-year-old child is taller than 125 cm. b. Find the probability that three randomly selected 9-year-old children are taller than 125 cm. c. Find the probability that the mean height of three randomly selected 9-year-old children is greater than 125 cm.