Question: The U.S. Bureau of the Census reported in Current Housing Reports that the mean livable square footage for single-family detached homes is 1742 square feet with a standard deviation of 560 sq. ft.

a. For random samples of 25 single-family detached homes, determine the mean and standard deviation of the distribution of the mean square footages of the homes.

b. For random samples of 25 single-family detached homes, determine the probability that the mean square footage is between 1630 sq. ft. and 1854 sq. ft.

c. Suppose that random samples of 400 single-family detached homes are obtained. Determine the mean and standard deviation of the distribution of the mean square footages of the homes.

d.  For random samples of 400 single-family detached homes, determine the probability that the mean square footage is between 1630 sq. ft. and 1854 sq. ft.

e.  For random samples of 400 single-family detached homes, determine the probability that the mean square footage is less than 1742 sq. ft.

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