Question

Suppose that, as part of a game at a charity carnival, players are invited to spin a wheel for a chance at winning either a small, medium, or large prize. The wheel is constructed so that the probability that a player does not win a prize, p, is 0.60. If a random sample of 40 players is selected, then p^ is the proportion of players in the sample who do not win a prize.

What is the mean of the sampling distribution of p^?

μp^=

What is the standard deviation of the sampling distribution of p^? Give your answer precise to three decimal places.

σp^=

Which of the following graphs shows the sampling distribution of p^?

Answer 1

Solution

Given that,

p = 0.60

1 - p = 1-0.60=0.40

n = 40

mean of the sampling distribution of p^

$\mu$_{$\hat p$} = p =0.60

standard deviation of the sampling distribution of p^

$\sigma$_{$\hat p$} =  $\sqrt$[p ( 1 - p ) / n] =  $\sqrt$ [(0.60*0.40) / 40 ] = 0.077