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Math Help - Help with normal distribution problem

  1. #1
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    Help with normal distribution problem

    Don't know how my friend got the z1=-1.28, z2=1.28. Everything else is clear

    The question:
    The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. If the standard deviation for the salaries of both genders is approximately $5200 and the salaries are normally distributed, find the 80th percentile salary for the male professors and female professors.
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  2. #2
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    Quote Originally Posted by gtgamer140@yahoo.com View Post
    Don't know how my friend got the z1=-1.28, z2=1.28. Everything else is clear

    The question:
    The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. If the standard deviation for the salaries of both genders is approximately $5200 and the salaries are normally distributed, find the 80th percentile salary for the male professors and female professors.

    For the first one,find a such that

    P\left( \frac{a-99,685}{5,200}\right) <0.8

    Apply the same technique for the second.
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  3. #3
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    Thank you for your reply but I am looking for an explanation on how my friend obtained the z1 and z2 values. I have attached a picture and circled in red what I meant.
    Attached Thumbnails Attached Thumbnails Help with normal distribution problem-100_0664.jpg  
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  4. #4
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    Then solve

    P(Z<x_1)= 0.1\implies x_1 = -1.2816

    Using symmetry x_2 =1.2816

    Look here http://davidmlane.com/hyperstat/z_table.html
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  5. #5
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    Thanks again for your post.
    I don't see where the 0.1 comes from
    Can you explain where exactly my friend gets the 1.2 and .8 from to add and get the separate z values? Everything except that is clear to me
    thankx again
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  6. #6
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    Quote Originally Posted by gtgamer140@yahoo.com View Post
    I don't see where the 0.1 comes from
    80% in the middle means 10% each side.
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  7. #7
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    Re: Help with normal distribution problem

    i also do not understand how you got the two z scores. and the answers that were on that persons sheet were wrong to find the 80th percentile you can just go to the TABLE E chart and find the z score that corresponds to .8 which is .7995 which is under .84 so you then times .84(5200)+99685 to get 104,053 and do the same for the female. i am just confused on how you got -1.28 and 1.28
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