7. Suppose that a particular brand of peanut butter is in factfavored by 47% of all moms. A consumer organization will take arandom sample of 200 moms from across the country and will use ˆp,the sample proportion, to estimate p, the actual proportion of momswho favor that peanut butter brand.
(a) Is it reasonable to assume that the sampling distribution ofˆp is approximately normal? Justify.
(b) Compute the mean and standard deviation of the ˆpdistribution. (Give your answer to four decimal places.)
(c) What is the approximate probability that the random samplewill produce a ˆp value greater than .5, causing the consumerorganization to incorrectly conclude that the majority of momsprefer this brand of peanut butter? (Give your answer to fourdecimal places.)
