Question

Suppose a large consignment of cell phones contained 19% defectives. If a sample of size 399 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 5%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

=  [p ( 1 - p ) / n] = [(0.19 * 0.81) / 399] = 0.0196

= P[ -0.05 / 0.0196 < ( - ) / < 0.05 / 0.0196]

= P(-2.55 < z < 2.55)

= P(z < 2.55) - P(z < -2.55)

= 0.9892