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Bob
Bob asked in Science & MathematicsMathematics · 7 years ago

Estimate the probability that if the company books 301 persons, not enough seats will be available?

An airline company is considering a new policy of booking as many as 301 persons on an airplane that can seat only 290. (Past studies have revealed that only 89% of the booked passengers actually arrive for the flight.)

I figured out that the mean is .89 * 301

I figured out the standard deviation is sqrt(.89 * 301 * .11)

Estimate the probability that if the company books 301 persons, not enough seats will be available.

I figure that (mean - 301)/(std) would give how many standard deviations away it is, and then what do I do with that number?

Can someone help me find the probability?

1 Answer

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  • Leonard
    Lv 7
    7 years ago

    So far, you are ok (but you have to standardize relative to 290, not 301). mean=267.89 and std dev=5.428.

    Now standardize - 290 seats is (290-267.89)/5.428=4.073 std dev above expected, which has a .000023

    chance of occurrence from normal table.

    Note - technically, you could use the 0.5 correction and calculate (290.5-267.89)/5.428 etc

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