Please help me solve the stat problem below.

Question

The ages of a group of 151 randomly selected adult females have a standard deviation of

16.416.4

years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let

sigmaσequals=16.4

years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want

99​%

confidence that the sample mean is within​ one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population?

The required sample size is:

Answer 1

99% confidence, alpha = 2.58

1/2 = 16.4/sqrt(N)

Multiplies both sides by 2*sqrt(N):

sqrt(N) = 16.4 *2

N = (32.8)^2 = 1075.84