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Math Help - Normal Distribution help

  1. #1
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    Normal Distribution help

    I am unsure how to finish this problem.
    " The weekly amount spent by a company for travel has approximately a normal distribution with mean = $550 and standard deviation = $40. What is the probability that the actual expenses will exceed $570 in 20 or more weeks during the next year? (Suppose there are 52 weeks next year.)

    I know this is an approximation of normal distribution binomial but am unsure how to set it up. I started with
    z= x-550/40, but am unsure of the next steps to take. Can anyone help explain the next steps to take? Thanks.
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  2. #2
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    Quote Originally Posted by chardukian View Post
    I am unsure how to finish this problem.
    " The weekly amount spent by a company for travel has approximately a normal distribution with mean = $550 and standard deviation = $40. What is the probability that the actual expenses will exceed $570 in 20 or more weeks during the next year? (Suppose there are 52 weeks next year.)

    I know this is an approximation of normal distribution binomial but am unsure how to set it up. I started with
    z= x-550/40, but am unsure of the next steps to take. Can anyone help explain the next steps to take? Thanks.
    Let X be the random variable amount spent (dollars) in a week.

    X ~ Normal (\mu = 550, \, \sigma = 40).

    Calculate p = Pr(X > 570) = Pr(Z > 1/2).


    Let Y be the random variable number of weeks in a year that exceed $570.

    Y ~ Binomial(p = calculated above, n = 52).

    Calculate \Pr(Y \geq 20). (The normal approximation is probably valid here).
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  3. #3
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    Thanks a lot.
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