8. There are 10 daily morning flights from New York to Toronto. Suppose, the pro

Question

8. There are 10 daily morning flights from New York to Toronto. Suppose, the probability that any flight arrives late is 0.10.

a) What is the probability that none of the flights is late today? (Hint: Binomial distribution, success=late and not success=not late) *Total flights =n=10, x refers to the number of successes, here x=0. *Use this formula P(x) = nCx Px(1-P)n-x and replace the values of n and x.

b) At least 8 flights will be late (Find probabilities of x=8, x=9 and x=10 and then add all these probabilities)

c) Maximum 2 flights will be late. (Hints: Find the probabilities of x=0, x=1 and x=2 and then add all these probabilities)

Explanation / Answer

(a) n = 10, p = 0.10, q = 0.90, x = 0

P(x) = nCx p^x q^(n - x)

P(0) = 10C0 0.10^0 0.90^10 = 0.3487

(b) P(x 8) = P(8) + P(9) + P(10) = 10C8 0.10^8 0.90^2 + 10C9 0.10^9 0.90^1 + 10C10 0.10^10 0.90^0 = 0

(c) P(x 2) = P(0) + P(1) + P(2) = 10C0 0.10^0 0.90^10+ 10C1 0.10^1 0.90^9 + 10C2 0.10^2 0.90^8 = 0.9298

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