How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 200 fellow students,finding a mean height of 166.6 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your classmates.

A) (163.73,169.27)
B) (164.04,169.16)
C) (165.992,167.01)
D) (164.02,168.98)
E) (164.91,170.09)

Using the formula for a confidence interval for a population mean with a known standard deviation and a 90% confidence level, we have:

Margin of error = z* (standard deviation / square root of sample size)
where z* is the z-score associated with the 90% confidence level, which can be found using a standard normal distribution table or calculator. For a two-tailed 90% confidence level, we have:

z* = 1.645

Plugging in the values from the problem, we get:

Margin of error = 1.645 * (5.64 / sqrt(15)) ≈ 2.31

Therefore, the 90% confidence interval for the mean height of the population of statistics classmates is:

166.6 ± 2.31

or

(164.29, 168.91)

Among the answer choices, the closest one to this interval is B, (164.04,169.16), so that is the best choice.