You need to estimate the mean useful life of a certain brand

You need to estimate the mean useful life of a certain brand of light bulb to within 20 hours with 98% confidence. Previous studies indicate that the standard deviation for the light bulb is 40 hours. How many observations should your sample contain to meet this desired level of accuracy?

Solution

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.02% LOS is = 2.33 ( From Standard Normal Table )
Standard Deviation ( S.D) = 40
ME =20
n = ( 2.33*40/20) ^2
= (93.2/20 ) ^2
= 21.72 ~ 22