An admissions director wants to estimate the mean age of all

An admissions director wants to estimate the mean age of all students enrolled at his college and he wants the estimate to be within six months of the true population mean. From past university reports, it is known the population standard deviation is approximately 3.4 years and ages are normally distributed. Calculate the minimum sample size for a confidence level of 95%.

Need step by step, please.

Solution

Compute Sample Size , Considering data in Year Format
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 3.4
ME =0.5 [ Year ]
n = ( 1.96*3.4/0.5) ^2
= (6.664/0.5 ) ^2
= 177.636 ~ 178