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Elementary Statistics: Quiz 7: The Central Limit Theorem

Module by: Susan Dean, Barbara Illowsky, Ph.D.

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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