According to an airline, flights on a certain route are on time 80% of the time.

Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 7 flights are on time. (c) Find and interpret the probability that fewer than 7 flights are on time. (d) Find and interpret the probability that at least 7 flights are on time. (e) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time

Explanation / Answer

n = 10

P = 0.8

A) This is a binomial experiment because it consists of n = 10 repeated trials.Each trial has a probability of P = 0.8 and each trials are independent of each other.

B) P(X = x) = nCx * px * (1 - p)n - x

P(X = 7) = 10C7 * (0.8)^7 * (0.2)^3 = 0.201

C) P(X < 7) = 1 - P(X >7)

= 1 - (P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10))

= 1 - (10C7 * (0.8)^7 * (0.2)^3 + 10C8 * (0.8)^8 * (0.2)^2 + 10C9 * (0.8)^9 * (0.2)^1 + 10C10 * (0.8)^10 * (0.2)^0 = 1 - 0.879

= 0.121

D) P(X > 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

=  10C7 * (0.8)^7 * (0.2)^3 + 10C8 * (0.8)^8 * (0.2)^2 + 10C9 * (0.8)^9 * (0.2)^1 + 10C10 * (0.8)^10 * (0.2)^0

= 0.879

E) P(5 < x < 7) = P (x = 5) + P(X = 6) + P (X = 7)

= 10C5 * (0.8)^5 * (0.2)^5 + 10C6 * (0.8)^6 * (0.2)^4 + 10C7 * (0.8)^7 * (0.2)^3 = 0.3158

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