Week 7: Quiz 7

Question 1

The Central Limit Theorem is important in statistics because:

• a. For any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.

• b. For any sized sample, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the distribution.

• c. As the sample size gets large enough, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

Question 2

Which of the following is true about the sampling distribution of the mean?

• a. The mean of the sampling distribution is always μ.

• b. The standard deviation of the sampling distribution is always σ.

• c. The shape of the sampling distribution of the mean is always approximately normal, regardless of the sample size.

Question 3

Suppose a sample of n = 25 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. What is the standard error of the mean?

• a. 6 ounces

• b. 2.5 ounces

• c. 0.5 ounces

Question 4

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

• a. 0.012 million

• b. 0.12 million

• c. 12 million

Question 5

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and a standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

• a. 0.300

• b. 0.003

• c. 0.200

Question 6

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

• a. approximately 0

• b. 0.0828

• c. 0.9772

Tutorial for Quiz 7