13. Whe a live person. You watch the random dialing machine made 15 calls. (hint

Question

13. Whe a live person. You watch the random dialing machine made 15 calls. (hint: Binomial distribution) n a survey calls a residential telephone numbers at random, only 20% of the calls reach Full Name pts each) a. What is the probability that 3 or fewer calls reach a person? (keep four decimal places) b. What is the probability that at least 2 calls reach a person? (keep four decimal places) c. For a sample of 15 calls, compute the expected number of calls that reaches a person. The average number of traffic accidents on a certain section of highway is two per week. Hint: Poisson distribution) 5 pts eac (keep four decim . Find the probability of exactly one accident during a one-week period.

Explanation / Answer

13) p = 0.2

n = 15

P(X = x) = 15Cx * 0.2x * (1 - 0.2)15-x

a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 15C0 * 0.20 * 0.815 + 15C1 * 0.21 * 0.814 + 15C2 * 0.22 * 0.813 + 15C3 * 0.23 * 0.812

                  = 0.6482

b) P(X > 2) = 1 - (P(X = 0) + P(X = 1))

                  = 1 - (15C0 * 0.20 * 0.815 + 15C1 * 0.21 * 0.814)

                  = 1 - 0.1671

                  = 0.8329

c) Expected value = n * p = 15 * 0.2 = 7.5

14) mean = 2 per week

P(X = x) = e-2 * 2x / x!

a) P(X = 1) = e-2 * 21 / 1! = 0.2707

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