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 15 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. (a) Determine whether this is a binomial experiment. (b) Find and interpret the probability that exactly 13 flights are on time. (c) Find and interpret the probability that at least 13 flights are on time. (d) Find and interpret the probability that fewer than 13 flights are on time. (e) Find and interpret the probability that between 12 and 14 flights, inclusive, are on time. (a) Does the probability experiment represent a binomial experiment?

Explanation / Answer

we apply the binomial theorm to solve the problem here.

Here are the answers with calc.

A. Yes. The variable wether flight comes on time is a 1 or 0 binomial variable

B. P(X=13) = 15C13 (.75^13)(.25^2) = .156

C. P(X>=13) =0.2361

D P(X<13) = 15C0 (.75^0)(.25^15)+..+ 15C13 (.75^13)(.25^2) = .7639

E P(12<=X<=14) = |P(X=14) - P(X=12)| = |0.06681-0.2252 = .158

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