I asked this before but got the same answer that was posted previously for this

Question

I asked this before but got the same answer that was posted previously for this one...but the answer is for exactly how many will be ontime... I need at least 32 to me on time.

Show all your work.
Include the name of the software you used, the function, and the inputs to it.
Express any probabilities rounded to 3-significant digits.
Explain what your results mean.

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”.

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

Explanation / Answer

Ans:

Binomial distribution:

n=40

p=probability of success=0.785

1-p=probability of failure=1-0.785=0.215

Using Excel function BINOMDIST:

P(k>=32)=1-P(k<=31)=1-BINOMDIST(31,40,0.785,TRUE)=0.4995

(upto three digit 0.500)

P(k>37)=1-P(k<=37)=1-BINOMDIST(37,40,0.785,TRUE)=0.00439

(upto 3 digit 0.004)

Yes, it is unusual,as P(k>37)<0.05

P(k<25)=P(k<=24)=BINOMDIST(24,40,0.785,TRUE)=0.00621

(upto three digit 0.006)

Yes, it is unusual,as P(k<25)<0.05

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