5. In a mid-size city in Texas, 21% of all cars on the road are made by Ford. Th

Question

5. In a mid-size city in Texas, 21% of all cars on the road are made by Ford. The Ford corporation is doing market research in the town and has a representative of theirs wait at the intersection of Main and State Streets. The Ford rep counts the number of cars that go by until she observes the first Ford. Let Y -the number of cars that go by until the first Ford is observed. (a) What is the distribution of Y? Write down the pmf. (b) Calculate E (Y) and SD (Y). (c) What is the probability that the rep observes (i) between 3 and 5 cars (inchusive)? (ii) more than 5 cars?

Explanation / Answer

a)

Y follows geometric distribution

p= 0.21

P(Y = k) = (1-p)^(k-1) p

= 0.79^(k-1)* 0.21

b)

E(Y) = 1/p= 1/0.21 = 4.761904

sd(Y) = sqrt((1-p)/p^2) = sqrt(0.79/0.21^2) = 4.2324735

c)

P(3 <= Y<= 5)

= P(Y<=5) - P(Y<=2)

= 0.69229-0.3759

=0.31639

P(Y> 5) = 1 - P(Y<= 5)

= 1 - 0.69229

=0.30771

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