The advertising department of a nationally circulated magazine wishes to estimate the mean age of.its subscribers to within 0.5 year with 90% confidence. if they estimate that the standard deviation of the ages of their subscribers is 5 years, find the required sample size.a. 165b. 17c. 271d. 45 1 points first question previous question question 14 of 30 next question last question

The correct answer is C) 271.

We first find the z-score associated with this confidence interval:
Convert 90% to a decimal:  90/100 = 0.9
Subtract from 1: 1 - 0.9 = 0.1
Divide by 2:  0.1/2 = 0.05
Subtract from 1:  1 - 0.05 = 0.95

Looking this value up in a z-table, we see that this number is the same distance from 1.64 and 1.65; therefore we will use 1.645.

Now we will use the following formula to calculate the sample size required:
[tex]n=(\frac{z_{\alpha/2}\times\sigma}{E})^2 \\ \\=(\frac{1.645\times5}{0.5})^2=270.6\approx 271[/tex]