Question

Suppose a large shipment of stereos contained 21% defectives. If a sample of size 348 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 4%? Round your answer to four decimal places.

Answer 1

Solution

$\sigma$_{$\hat p$} =  $\sqrt$[p ( 1 - p ) / n] = $\sqrt$ [(0.21 * 0.79) / 348 ] = 0.0218

P(sample proportion will differ from the population proportion by more than 4%)

= 1 - P[ -0.04 / 0.0218 < ( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$} < 0.04 / 0.0218]

= 1 - P(-1.83 < z < 1.83)

= 1 - 0.9327

= 0.0673