A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation $\sigma = 20$ hours.
Find the sample size needed so that a $98 \%$ confidence interval for the mean lifetime will have a margin of error of 8 .
A) 117
B) 5
C) 6
D) 34

Question

Quizplus · Accepted Answer

To find the sample size $ n $, use the formula for margin of error $ E = z \times \frac{\sigma}{\sqrt{n}} $. For a 98% confidence level, $ z \approx 2.33 $. Set $ E = 8 $ and solve for $ n $: $ 8 = 2.33 \times \frac{20}{\sqrt{n}} $. Solving gives $ n \approx 34 $.

A Simple Random Sample of Kitchen Toasters Is to Be σ=20\sigma = 20σ=20

A Simple Random Sample of Kitchen Toasters Is to Be $\sigma = 20$