Question

The average lifetime of batteries of a particular brand are known to be normally distributed with a standard deviation 8 hours. How large a sample size would be required to estimate the average lifetime within 2 hours with a 95% confidence?

If you get a decimal in your answer, always round it up for the sample size.

Answer 1

Solution:
Given in the question
Population standard deviation() = 8
Margin of error (E) = 2
Confidence level = 0.95
Level of significance() = 1 - Confidence level = 1 - 0.95 = 0.05
/2 = 0.05/2 = 0.025
From Z table we found Z/2 = 1.96
Sample size can be calculated as
n = (Z/2 * /E)^2 = (1.96*8/2)^2 = 7.84*7.84 = 61.4656 or 62
Sample size n = 62
So Sample size would be 62 required to estimate the average lifetime within 2 hours with a 95% confidence.