Determine the sample size needed in order to be 99 percent c

Determine the sample size needed in order to be 99 percent confident the p, the sample proportion of ColorSmart-5000 television sets that last at least five years without a single repair, is within 0.03 of p, the true proportion of sets that last at least five years without a single repair.

Solution

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Samle Proportion = 0.5
ME = 0.03
n = ( 2.576 / 0.03 )^2 * 0.5*0.5
= 1843.271 ~ 1844