According to an airline, flights on a certain route are on time 75% of the time.

Question

According to an airline, flights on a certain route are on time 75% of the time. Suppose 9 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. Determine whether this is a binomial experiment. Find and interpret the probability that exactly 7 flights are on time. Find and interpret the probability that at least 7 flights are on time. Find and interpret the probability that fewer than 7 flights are on time. Find and interpret the probability that between 6 and 8 flights, inclusive, are on time.

Explanation / Answer

a. As each flight has the same probability of being on time (0.75) and the punctuality of flights are independent of each other as they are selected randomly, the given experiment is a binomial experiment.

b. P(X=7) = 9C7 *(0.75)7 * (1-0.75)9-7 = 0.30

There is 30% chance that 7 out of 9 flights are on time.

c. P(X>=7) = P(X=7) + P(X=8) + P(X=9)

= 9C7 *(0.75)7 * (1-0.75)9-7 + 9C8 *(0.75)8 * (1-0.75)9-8 + 9C9 *(0.75)9 * (1-0.75)9-9

= 0.60

There is 60% chance that atleast 7 out of 9 flights are on time.

d. P(X<7) = 1 - P(X>=7) = 1 - 0.60 = 0.40

There is 40% chance that less than 7 out of 9 flights are on time.

e. P(6<=X<=8) = P(X=6) + P(X=7) + P(X=8)

= 9C6 *(0.75)6 * (1-0.75)9-6 + 9C7 *(0.75)7 * (1-0.75)9-7 + 9C8 *(0.75)8 * (1-0.75)9-8

= 0.76

There is 76% chance that 6 to 8 (both inclusive) flights are on time.

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