Question

A bottle maker assumes that 18% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 626 bottles would differ from the population proportion by more than 4%? Round your answer to four decimal places.

Answer 1

Using normal approximation,

P( $\hat{p}$ < p) = P( Z < $\hat{p}$ - p / sqrt( p( 1 - p) / n) )

So,

We have to calculate P( $\hat{p}$ > p+0.04) = ?

= P( $\hat{p}$ > 0.18 + 0.04) = ?

P( $\hat{p}$ > 0.22) = P( Z > 0.22 - 0.18 / sqrt( 0.18 * 0.82 / 626) )

= P( Z > 2.6050)

= 0.0046