According to an airline, flights on a certain route are on time 95%of the time.

Question

According to an airline, flights on a certain route are on time 95%of the time. Suppose 20 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities.

(a) Determine whether this is a binomial experiment.

(b) Find and interpret the probability that exactly 18 flights are on time.

(c) Find and interpret the probability that at least18 flights are on time.

(d) Find and interpret the probability that fewer than 18 flights are on time.

(e) Find and interpret the probability that between 16 and 18 flights, inclusive, are on time.

Explanation / Answer

a) Yes, this is a binomial distribution because:

--> There are finite number of trials (n = 20).

--> The trials are independent of each other.

--> There are only two possible outcomes: Flight on time (Success) or flight not on time (Failure)

--> The probability of success remains same for all trials.

From technology output (Rounded off to 4 decimal places),

b) P(X = 18) = 0.1887

c) P(X > 18) = 0.9245

d) P(X < 18) = 0.0755

e) P(16 < X < 18) = 0.2616

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