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, rho, is 0.60. If a random sample of 40 players is selected, then p^Hat is the proportion of players in the sample who do not win a prize. What is the mean of the sampling distribution of p^Hat? mu _p^Hat = Number _______ What is the standard deviation of the sampling distribution of p^Hat? Give your answer precise to three decimal places. sigma _p^Hat = Number _______
Accepted Solution
A:
Answer:[tex]\mu_{\^{p}} = 0.6[/tex] and [tex]\sigma_{\^{p}} \simeq 0.49[/tex]Step-by-step explanation:According to the question,[tex]\^{p}[/tex] is the random variable 'Proportion of players in the sample who do not win a prize'.Now, here P(A player do not win a prize) = 0.6So, [tex]E(\^{p}) = \mu_{\^{p}} = 0.6[/tex]and [tex]Var(\^{p}) = 0.6 \times (1 - 0.6)[/tex] = [tex]0.6 \times 0.4[/tex] = 0.24so, [tex]\sigma_{\^{p}}[/tex] = [tex]\sqrt {0.24}[/tex] = [tex]\simeq 0.49[/tex]