1. Suppose we are interested in households who will buy a high-end automobile. W

Question

1.      Suppose we are interested in households who will buy a high-end automobile. We know the following information. We have seen that of the households that make over $100,000 per year ten percent (i.e. probability of .1) will buy a high-end automobile. Let X be defined as the number of households in the 3 we surveyed that indicate they intend to buy a high-end automobile. Assume we are surveying only households making over $100,000 per year.

a.       Using the binomial formula, compute the probability distribution for X.

b.      What is the chance that at least 1 household will indicate they intend to buy a high-end automobile?

c.       Suppose we now survey 1000 households making over $100,000 per year. How many of these households do we expect to tell us that they will intend to buy a high-end automobile?

d.      Suppose again we now survey 1000 households making over $100,000 per year. What is the standard deviation of the number of households that tell us they intend to buy a high-end automobile?

Explanation / Answer

p = 0.1

n = 3

a) P(X = x) = 3Cx * 0.1x * (1 - 0.1)3-x

b) P(X > 1) = 1 - P(X = 0)

                  = 1 - 3C0 * 0.10 * 0.93

                  = 1 - 0.729

                  = 0.271

c) n = 1000

Expected = n * p = 0.1 * 1000 = 100

d) Standard deviation = sqrt(n * p * (1 - p)) = sqrt(1000 * 0.1 * 0.9) = 9.5

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