Of the next 40 Tailhook flights arriving at your airport what is the probability

Question

Of the next 40 Tailhook flights arriving at your airport what is the probability that at least 32 of them will be on time?

What is the name of the software you used, the function, and the inputs to it? Express any probabilities rounded to 3-significant digits.

On Time Flights The U.S. Department of Transportation's (DOT) Bureau of Transportation Statistics (BTS) publishes its “Air Travel Consumer Report” every month, reporting what percentage of major carrier flights are on time. As noted at www.transportation.gov, “The rule requires carriers to currently report on operations to and from the 30 U.S. airports that account for at least one percent of the nation's total domestic scheduled-service passenger enplanements.” “A flight is counted "on time" if it operated less than 15 minutes after the scheduled time shown in the carriers' Computerized Reservations Systems (CRS).” Let us assume that one of the carriers at your regional airport is Tailhook Airlines, a newer airline that has quickly become known for hiring ex-Navy pilots and providing exciting flights. You note that Tailhook’s on-time average is 78.5% in the DOT’s latest “Air Travel Consumer Report”.

Explanation / Answer

Probability of on-time = p=0.785

q= 0.215

P( X>=32) = SUm of binomials [ 40Cr p^r q^(40-r)] where r varies from 32 to 40 =0.49950887075

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