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7 April, 17:02

John Goodie is doing his budget. He discovers that he has spent an average of $235.00 a month on food for the year with a standard deviation of $55.00. What percent of his monthly expenses for this category would he expect to fall between $147.00 and $202.00?

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  1. 7 April, 20:25
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    He would expect his monthly expenses for food to fall between $147.00 and $202.00 with a probability of 21.95%

    (the wording of the question should be something like "What percent would he expect his monthly expenses for this category to fall between $147.00 and $202.00?)

    Explanation:

    Assume that his spending on food follows standard distribution

    The probability that his expenses would be from 147.00 to 235.00 is given by f (z)

    z = (235.00 - 147.00) / 55 = 1.6 = > f (z) = 0.4452 (44.52%)

    (z is the z-score)

    The probability that his expenses would be from 202.00 to 235.00 is given by f (z)

    z = (235.00 - 202.00) / 55 = 0.6 = > f (z) = 0.2257 (22.57%)

    So the probability that his expenses would be from $147.00 to $202.00 is

    44.52% - 22.57% = 21.95%
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