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# Answered: Central Limits and Probabilities

Question 1

The Central Limit Theorem is important in statistics because

Select one:

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?

Select one:

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?

Select one:

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?

Select one:

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?

Select one:

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.

Select one:

a.

approximately 0

b.

0.0828

c.

0.9772

Question 7.

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimetre and a standard deviation of 0.1 centimetre. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

Select one:

a.

0.029

b.

0.050

c.

0.091

Question 8

The average score of all pro-golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 pro-golfers played the course today. Find the probability that the average score of the 36 pro-golfers exceeded 71.

Select one:

a.

0.228

b.

0.0228

c.

0.00228

Question 9

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of 9 tennis balls, what is the probability that the sample mean is less than 2.61 inches?

Select one:

a.

0.228

b.

0.772

c.

0.0228

Question 10

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches?

Select one:

a.

0.0682

b.

0.6827

c.

0.3173

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