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24 February, 22:00

The amount of 60 t-shirts has a normal distribution with a mean of $12 and standard deviation of $2. What percentage of the bills were between $10 and $14?

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  1. 25 February, 00:33
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    Step-by-step explanation:

    The formula for normal distribution is expressed as

    z = (x - u) / s

    Where

    x = cost of T - shirts

    u = mean cost

    s = standard deviation

    From the information given,

    u = $12

    s = $2

    We would determine the probability of the bills that were between $10 and $14. It is expressed as

    P (10 lesser than x lesser than or equal to 14)

    For x = 10,

    z = (10 - 12) / 2 = - 2/2 = - 1

    Looking at the normal distribution table, the corresponding z score is 0.15866

    For x = 14,

    z = (14 - 12) / 2 = 2/2 = 1

    Looking at the normal distribution table, the corresponding z score is 0.84134

    P (10 lesser than x lesser than or equal to 14) = 0.84134 - 0.15866 = 0.68268

    The percentage of the bills that were between $10 and $14 is

    0.68268*100 = 68.3%
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