Question

A company that produce soap wants to estimate the mean amount of the excess weight of soap in a “1000-gram” bottle at a 99% confidence. The company knows that the standard deviation of the excess weight in all such soap bottles is 169 grams. How large a sample should the company select so that the estimate is within 1.5 grams of the population mean?

Answer 1

Solution :

Given that,

standard deviation =s =   =169

Margin of error = E = 1.5

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576

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

n = ( 2.576* 169 / 1.5 )2

n =84233.065

Sample size = n =84233 rounded