Question

30% of a gardener's tulips are orange.

If the gardener randomly picked 50 tulips, what is the probability that more than 36% of the tulips she picks will be orange?

Answer 1

Solution

$\sigma$_{$\hat p$} =  $\sqrt$[p( 1 - p ) / n] = $\sqrt$ [(0.30 * 0.70) / 50 ] = 0.0648

P( $\hat p$ > 0.36) = 1 - P( $\hat p$ < 0.36)

= 1 - P(( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$} < (0.36 - 0.30) / 0.0648)

= 1 - P(z < 0.93)

= 0.1762

Probability = 0.1762