Question

2. A bank believes that 97% of its loan applicants will repay their loans. You take a SRS of 400 loan applicants. What’s the chance that fewer than 96% in the sample will repay their loans? Show your work.

Answer 1

Given,

p = 0.97, n = 400

We have to calculate P( $\hat{p}$ < 0.96) = ?

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

= P( $\hat{p}$ < 0.96) = P( Z < 0.96 - 0.97 / sqrt( 0.97 * 0.03 / 400)

= P( Z <-1.1724)

= 1 - P( Z < 1.1724)

= 1 - 0.8795

= 0.1205