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7 January, 09:24

In an inventory of standardized weights, 8% of the weights are found to exceed 10.282 grams and 6% weighs below 9.69 grams. If weight is a continuous random variable distributed normally, find the mean and standard deviation for this distribution.

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  1. 7 January, 11:47
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    Step-by-step explanation:

    We are given here for the random variable X:

    P (X > 10.282) = 0.08 and P (X < 9.69) = 0.06

    From standard normal tables, we have:

    P (Z 1.405) = 0.08

    Therefore, the z score of 10.282 is 1.405

    Therefore, Mean + 1.405*Std Dev = 10.282

    Also from standard normal tables, we have:

    P (Z < - 1.555) = 0.06

    Therefore, Mean - 1.555*Std Dev = 9.69

    Subtracting the second equation from first, we get here:

    Std Dev (1.405 + 1.555) = 10.282 - 9.69

    Std Dev = 0.2

    Now the mean can be computed as:

    Mean = 1.555*Std Dev + 9.69 = 1.555*0.2 + 9.69 = 10.001

    Therefore 10.001 is the required mean and 0.2 is the required standard deviation for the distribution here.
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