Question

Suppose a large shipment of microwave ovens contained 11% defectives.

If a sample of size 247 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%? Round your answer to four decimal places.

Answer 1

Solution

=  [p ( 1 - p ) / n] = [(0.11 * 0.89) / 247 ] = 0.0199

P(the sample proportion will differ from the population proportion by less than 3%)

= P[ -0.03 / 0.0199 < ( - ) / < 0.03 / 0.0199]

= P(-1.51 < z < 1.51)

= P(z < 1.51) - P(z < -1.51)

= 0.8690