Elementary Statistics: Quiz 7: The Central Limit Theorem
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.
Exercise 1
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.
Exercise 2
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
Exercise 3
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
Exercise 4
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
Exercise 5
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
Exercise 6
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
Exercise 7
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
Exercise 8
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
Exercise 9
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
Exercise 10
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.
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Last edited by James Cooper on Oct 24, 2008 6:41 pm GMT-5.