Summary: This module is a quiz containing 10 multiple choice questions covering topics related to the central limit theorem. This module is part of a set of companion resources to Collaborative Statistics (col10522) by Barbara Illowsky and Susan Dean.

Given that X ~ N(300, 15), we survey 20 at a time and are interested in the distribution of X-bar. As the number of data values averaged together gets larger, what happens to the standard error of the mean (the standard deviation of X-bar)?

**A.**It becomes larger.**B.**It becomes smaller.**C.**It approaches the average of X-bar.**D.**It approaches the standard deviation of X.

Given X ~ Exp(1/8), we survey 100 at a time and are interested in the distribution of X-bar. Find the standard deviation of X-bar.

**A.**0.8**B.**0.0125**C.**0.0800**D.**0.125

Given X ~ Exp(1/8), we survey 100 at a time and are interested in the distribution of X-bar. Find the third quartile of X-bar.

**A.**6**B.**0.6321**C.**8.54**D.**2.30

Given that X ~ N(300, 15), we survey 20 at a time and are interested in the distribution of X-bar. Find the 33rd percentile of the distribution for X-bar.

**A.**298.6**B.**293.5**C.**301.4**D.**100.0

Given that X ~ N(300, 15), we survey 20 at a time and are interested in the distribution of X-bar. Find the z-score associated with x-bar = 290.

**A.**-10/15**B.**-10**C.**-2.9814**D.**-13.3333

Given X ~ Exp(0.125), we survey 100 at a time and are interested in the distribution of X-bar. P(X-bar < 7)= ____________.

**A.**0.1056**B.**0.5831**C.**0.9987**D.**0.0001

Given X ~ U(2,18), we survey forty at a time and are interested in the distribution of X-bar. The standard deviation of X-bar is:

**A.**1.5811**B.**0.1155**C.**0.7303**D.**4.62

Given X ~ U(2,18), we survey forty at a time and are interested in the distribution of X-bar. P(X < 4) is ______ P(X-bar < 4).

**A.**less than**B.**equal to**C.**greater than**D.**at most

Given X ~ U(2,18), we survey forty at a time and are interested in the distribution of X-bar. P(2 < X < 18) is _______ P(2 < X-bar < 18)

**A.**less than**B.**equal to**C.**greater than**D.**at most

Given that X ~ N(300, 15), we survey 20 at a time and are interested in the distribution of X-bar. What can be said about the median of the random variable X-bar?

**A.**It is the same as the median of X.**B.**It is the same as the average of X-bar.**C.**It is the same as the average of X.**D.**A, B, C are all correct.