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For Exercises 4.90 and 4.91, see page 212; for 4.92, see page 214; and for 4.93, see page 216.

Question 4.91

4.91 How many cars?

Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ignore the few households that own more than five cars:

Number of cars X 0 1 2 3 4 5
Probability 0.09 0.36 0.35 0.13 0.05 0.02
  1. Verify that this is a legitimate discrete distribution. Display the distribution in a probability histogram.
  2. Say in words what the event {X1} is. Find P(X1).
  3. Your company builds houses with two-car garages. What percent of households have more cars than the garage can hold?

4.91

(a) 0.09+0.36+0.35+0.13+0.05+0.02=1. It is a legitimate discrete distribution. (b) The American household owns at least one car. P(X1)=0.91. (c) 20%.

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