Question

please help me compute the final step to this question, and if possible be as detailed as you can, I am unsure what step I am messing up.

Suppose 6% of students are veterans and 126 students are involved in sports. How unusual would it be to have no more than 12 veterans involved in sports? (12 veterans is about 9.5238%) When working with samples of size 126, what is the mean of the sampling distribution for the proportion of veterans? 0.06 When working with samples of size 126, what is the standard error of the sampling distribution for the proportion of veterans? 0.021157009 OM Compute P(P < 0.095238). PP < 0.095238) = NOTE: Give results accurate to 5 decimal places

Answer 1

Solution

$\sigma$_{$\hat p$} =  $\sqrt$[p ( 1 - p ) / n] = 0.021157009

P( $\hat p$ $\le$ 0.095238) =

= P[( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$}$\le$ (0.095238 - 0.06) / 0.021157009]

= P(z$\le$1.666)

= 0.9521