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Statistic

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An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%.

  • Statistic -

    Use the normal approximation to the binomial distribution.

    mean = np
    standard deviation = √npq

    Therefore:
    mean = .94n
    standard deviation = √(n)(.94)(.06) = √(.0564n)

    Using z-scores:
    z = (x - mean)/sd
    With the data:
    1.645 = (160 - .94n)/√(.0564n)

    Solve for n.

    (Hint: Round answer to 165.)

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