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    Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.

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    Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.
    a) What is the probability that a randomly selected customer spends less than $35 at this store?
    b) What is the probability that a randomly selected customer spends between $15 and $35 at this store?
    c) What is the probability that a randomly selected customer spends more than $10 at this store?
    d) Find the dollar amount such that 75% of all customers spend no more than this amount?
    e) Find the dollar amount such that 80% of all customers spend at least this amount?
    f) Find two dollar amounts, equidistant from the mean of $25, such that 90% of all customer purchases are between these values?

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    Solution Preview

    Please see the attached file.

    Suppose the purchase amount is X. Then the mean of X is m=25 and the standard deviation of X is d=8
    Now let Y=(X-25)/8, then Y follows the standard normal distribution and X=8Y+25.
    The following calculation will be done by the normal standard ...

    Solution Summary

    Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.

    $2.19

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