Question

Based on past experiences, a bank believes that 10% of the people who receive loans will not make payments on time. The bank has recently approved 250 loans. What’s the probability that over 12% of these clients will not make timely payments? Give your answer to 4 decimal places.

Answer 1

Solution

$\sigma$_{$\hat p$} =  $\sqrt$[p( 1 - p ) / n] = $\sqrt$ [(0.10 * 0.90) / 250 ] = 0.019

P( $\hat p$ > 0.12) = 1 - P( $\hat p$ < 0.12)

= 1 - P(( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$} < (0.12 - 0.10) / 0.019)

= 1 - P(z < 1.054)

= 0.1459

Probability = 0.1459