Benny wants to estimate the mean lifetime of Energizer batteries, with a confidence level of 97%, and with a margin of error not exceeding ±10 hours. If the standard deviation of the lifetime is known to be 55 hours, how many batteries does Benny need to sample?

143 batteries does Benny need to sample

Explanation:

Given data

confidence level = 97%

error = ±10 hours

standard deviation SD = 55 hours

to find out

how many batteries does Benny need to sample

solution

confidence level is 97%

so a will be 1 - 0.97 = 0.03

the value of Z will be for a 0.03 is 2.17 from standard table

so now we calculate no of sample i. e

no of sample = (Z * SD / error) ²

no of sample = (2.16 * 55 / 10) ²

no of sample = 142.44

so 143 batteries does Benny need to sample