Big Y sells two different coffee makers: a basic model for $30, and a fancier model for $50. We assume that different buyers’ choices don’t affect each other, and that different buyers share the same (constant) probability for whether they choose the cheapo model or the fancy one. (a) Suppose that we observe the next 25 people buying coffee makers. Let X be the number of people among the 25 who opted for the fancy coffee maker. What is the distribution of X? Why might this be an unrealistic
Big Y sells two different coffee makers: a basic model for $30, and a fancier model for $50. We assume that different buyers’ choices don’t affect each other, and that different buyers share the same (constant) probability for whether they choose the cheapo model or the fancy one. (a) Suppose that we observe the next 25 people buying coffee makers. Let X be the number of people among the 25 who opted for the fancy coffee maker. What is the distribution of X? Why might this be an unrealistic description of the situation? (b) Let h(X) be the total revenue Big Y receives from the 25 people. Find the mean and standard deviation of h(X). (c) Big Y estimates that, because of effective marketing, customers have a 65% chance of choosing the expensive coffee maker over the cheap one. If the store sells 100 coffee makers on a given day, use the central limit theorem to calculate the approximate probability that the total revenue will be higher than $4500.
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