A qualitycontrol engineer wants to estimate the mean fill we

A quality-control engineer wants to estimate the mean fill weight of boxes that have been filled with cereal by a certain machine on a certain day. He draws a simple random sample of 100 boxes from the population of boxes that have been filled by that machine on that day. He computes the sample mean fill weight to be X = 12.05 oz, and the sample standard deviation to be s = 0.1 oz. How many boxes must be sampled to obtain a 68% confidence interval of width

Solution

Answer to the question)

For 68% the value of z = 1

we got s = 0.1

and error = 0.012

.

Thus the formula of sample size is

n = ( z * s / e)^2

.

on plugging the vlaues we get

n = (1 * 0.1 /0.012)^2

n = 69.44 ~ 70

Thus the sample size must be 70