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29 January, 09:48

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?

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  1. 29 January, 11:01
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    0.0323 = 3.23%. Is unusual

    Step-by-step explanation:

    Using the normal distribution we can find z value with the mean and standard deviation as follows. x is the value we want to know its probability

    z = (x - mean) / standard deviation

    z = (5-8.54) / 1.91

    z = - 1.85

    Using z tables for normal distribution, for z = 1.85, we have an area under the curve of 0.9677. Since we want to know the probability for 5 minutes or less, we have to substract from

    p = 1 - 0.9677

    p = 0.0323

    An event with a probability less than 5% is considered unusual.
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