Name:    Unit 07-06 - Sample Quiz: Central Limit Theorem

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

 The graph at the right show the frequency distribution of a population with a population mean of 4 and a population standard deviation of 2.5.If samples of size 25 (n =25) were taken from the population what would be the mean of the sample means ?
 a. 0.8 c. 4 b. 1.5 d. 6.5

2.

 The graph at the right show the frequency distribution of a population with a population mean of 2.5 and a population standard deviation of 3.If samples of size 36 (n =36) were taken from the population what would be the standard deviation of the sample means ?
 a. c. b. d.

3.

 The graph at the right show the frequency distribution of a population with a population mean of 2.5 and a population standard deviation of 3.If samples of size 25 (n =25) were taken from the population which graph would most likely be a good representation of the distribution of the sample means?
 a. c. b. d.

4.

 A high school student spends an average of 6 hours  () on their phone a day with a standard deviation of 2.5 hours ().If samples of size 16 (n =16) were taken from the population what would be the mean of the sample means ?
 a. 1.5 c. 4 b. 2.5 d. 6

5.

 Use the central limit theorem if possible.  For a sample of n = 36, find the probability of a sample mean being greater  than 43 given and . The population is also normally distributed.

(Hint: First determine and and use those values to find )

 a. 0.3085 c. 0.5332 b. 0.4668 d. 0.6915

6.

 Use the central limit theorem if possible.  For a sample of n = 9, find the probability of a sample mean being less than 7  given and . The population is not normally distributed.
 a. 0.1587 c. 0.8413 b. 0.3694 d. Cannot be determined because the sample size is too small.

7.

 At a restaurant near the high school, the restaurant manager has determined that each customer on average spends \$9.10 ( ) with a standard deviation of \$3.00 (). The customer data was normally distributed.A group of 4 friends (n = 4) went to the restaurant together and one of the friends bought lunch for entire group. What is the probability that the total bill will be more than \$40? (Hint: This suggests finding the probability that the sample mean would be greater than \$10.00.)
 a. 12.8% c. 38.2% b. 27.4% d. 42.1%

8.

 The length of pregnancies are normally distributed with a mean of 268 days ( ) and a standard deviation of 15 days ().A group of 36 pregnant women  (n = 36) were in a parenting class together.  What is the probability that the average pregnancy for the women lasted longer than 270 days?
 a. 21.2% c. 55.2% b. 28.8% d. 78.8%