Question

Suppose the total snowfalls per year in a city are normally distributed. If the population standard deviation is 13 inches, what minimum sample size is needed to be 95% confident that the sample mean is within 4 inches of the true population mean?

Answer 1

Answer: 41

Step-by-step explanation:

Given : Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Margin of error : $E=4$

Standard deviation: $\sigma=13$

The formula to find the sample size : $n=(\dfrac{\sigma\times z_{\alpha/2}}{E})^2$

Then, we have

$n=(\dfrac{13\times(1.96)}{4})^2=40.5769\approx41$

Hence, the minimum sample size needed= 41.