Question

10) It is generally believed that the heights of adults males in the U.S. are approximately normally distributed with mean 70 inches (5 feet, 10 inches) and standard deviation 3 inches.

d) What proportion of men are between 64” and 76”? Provide a shaded sketch and calculator documentation.

e) A researcher takes a thousand samples each of size 30. For each sample, she computes the mean of the sample. What does the sampling distribution she created look like?

Shape of the sampling distribution: ______________________

Center of the sampling distribution: _____________________

Spread of the sampling distribution: ____________________ (some work required.)

f) What is the name of the famous statistical idea/principle that allows us to answer (e) above. [2pt]

________ ___________________ ______________________ __________________________

g) What effect does increasing the sample sizes have on the center of the distribution? [2pt]

i. It increases the center of the distribution. ii. It decreases the center of the distribution. iii. It has no effect on the center of the distribution.

h) What effect does increasing the sample sizes have on the spread of the distribution? [2pt]

a. It increases the spread of the distribution.

b. It decreases the spread of the distribution.

c. It has no effect on the spread of the distribution.

Answer 1