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22 February, 06:15

The monthly income of 5,000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1,250 and the standard deviation is $250. a) How many workers earn more than $1500 per month? b) How many workers earn less than $750 per month? c) What percentage of the workers earn between $750 and $1500 per month? d) What percentage of the workers earn less than $1750 per month?

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  1. 22 February, 08:00
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    a) 15.86

    b) 2.28%

    c) 81.86%

    d) 97.72%

    Explanation:

    we normalize to N (1; 0)

    Z = (X - u) / o

    being u the mean

    and o the standard deviation

    a)

    Z (1 - (1500 - 1250) / 250) = 0.158655254

    b)

    Z (750-1250) / 250 = 0.022750132

    c)

    Z ((1500 - 1250) / 250) - Z (750) = 0.841344746 - 0.022750132 =

    0.818594614

    d)

    Z (1750 - 1500) / 250 = 0.977249868
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