Question

If the standard deviation of the lifetime of washing machines is assumed to be 500 hours of use, how large of a sample must be taken to be 90% confident that an estimate of the population Mean hours of use will have a margin of error of not more than 50 hours?

Answer 1

Solution :

Given that,

standard deviation = =500

Margin of error = E = 50

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = ( 1.645 * 500 / 50 )2

n =270.6025

Sample size = n =271 rounded