3.6 Quiz 7: the central limit theorem

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.