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Math Help - job probability.....problem

  1. #1
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    Question job probability.....problem

    John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other.


    Referring to Table 6-4, for a given month, what is the probability that John's total income from these two jobs is less than $825?

    The answer is .0668

    The toal mean is 900 and total Std is 50


    My question is how did they come up with the total mean and std?
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  2. #2
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    Quote Originally Posted by Blevil View Post
    John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other.


    Referring to Table 6-4, for a given month, what is the probability that John's total income from these two jobs is less than $825?

    The answer is .0668

    The toal mean is 900 and total Std is 50


    My question is how did they come up with the total mean and std?
    Let X be the random variable 'monthly commission from day job (dollars)'.
    X ~ Normal (\mu_X = 600, \, \sigma_X = 40).

    Let Y be the random variable 'monthly income from night job (dollars)'.
    Y ~ Normal (\mu_Y = 100, \, \sigma_Y = 30).

    Let U = X + Y.

    It's well know that when X and Y are independent normal variates, then U ~ Normal (\mu = \mu_X + \mu_Y, \, \sigma^2 = \sigma^2_X + \sigma^2_Y) (so I disagree with "total mean is 900").

    So U ~ Normal (\mu = 700, \, \sigma = .....) and your job is to calculate Pr(U < 625).
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