In the following problem, check that it is appropriate to usethe normal approximation to the binomial. Then use the normaldistribution to estimate the requested probabilities.
What's your favorite ice cream flavor? For people who buy icecream, the all-time favorite is still vanilla. About 20% of icecream sales are vanilla. Chocolate accounts for only 9% of icecream sales. Suppose that 185 customers go to a grocery store inCheyenne, Wyoming, today to buy ice cream. (Round your answers tofour decimal places.)
(a) What is the probability that 50 or more will buyvanilla?
(b) What is the probability that 12 or more will buychocolate?
(c) A customer who buys ice cream is not limited to onecontainer or one flavor. What is the probability that someone whois buying ice cream will buy chocolate or vanilla? Hint:Chocolate flavor and vanilla flavor are not mutually exclusiveevents. Assume that the choice to buy one flavor is independent ofthe choice to buy another flavor. Then use the multiplication rulefor independent events, together with the addition rule for eventsthat are not mutually exclusive, to compute the requestedprobability.
(d) What is the probability that between 50 and 60 customerswill buy chocolate or vanilla ice cream? Hint: Use theprobability of success computed in part (c).
