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12 January, 18:44

The baggage limit for an airplane is set at 100 pounds per passenger. thus, for an airplane with 200 passenger seats there would be a limit of 20,000 pounds. the weight of the baggage of an individual passenger is a random variable with a mean of 95 pounds and a standard deviation of 35 pounds. if all 200 seats are sold for a particular flight, what is the probability that the total weight of the passengers' baggage will exceed the 20,000-pound limit?

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  1. 12 January, 18:47
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    At a mean of 95 pounds per passenger and standard deviation of 35 pounds, multiplying this with the total number of passengers = 200, results in:

    absolute mean = 95 * 200 = 19,000

    absolute std dev = 35 * 200 = 7,000

    Calculating for the z score:

    z = (x - u) / s

    where x is sample value = more than 20,000; u is the sample mean = 19,000; s is std dev = 7,000

    z = (20,000 - 19,000) / 7,000

    z = 0.143

    From the distribution tables,

    P (z = 0.14) = 0.5557

    Therefore a 55.57% chance that it will be more than 20,000 pound limit
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