Question

State police believe that 68% of the drivers drive above the speed limit on the freeway. Driving behavior of a random sample of 110 drivers were observed with hidden cameras. What is the probability that in that sample more than 71% of the drivers crossed the speed limit? Answer to 4 decimal places

Answer 1

Solution

Given that,

p = 0.68

1 - p = 1-0.68=0.32

n = 110

$\mu$_{$\hat p$} = p =0.68

$\sigma$_{$\hat p$} =  $\sqrt$[p( 1 - p ) / n] = $\sqrt$ [(0.68*0.32) / 110 ] = 0.044

P( $\hat p$ > 0.71) = 1 - P( $\hat p$ <0.71 )

= 1 - P(( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$} < (0.71-0.68) / 0.044)

= 1 - P(z <0.68 )

Using z table

= 1 -0.7517

=0.2483