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18 September, 23:15

The diameters of ball bearings are distributed normally. The mean diameter is 104 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 109 millimeters. Round your answer to four decimal places.

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  1. 18 September, 23:32
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    Answer: The probability that the diameter of a selected bearing is greater than 109 millimeters is 0.047

    Step-by-step explanation:

    Since the diameters of ball bearings are distributed normally, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = the diameters of ball bearings.

    µ = mean diameter

    σ = standard deviation

    From the information given,

    µ = 104 millimeters

    σ = 3 millimeters

    The probability that the diameter of a selected bearing is greater than 109 millimeters is expressed as

    P (x > 109) = 1 - P (x ≤ 109)

    For x = 109,

    z = (109 - 104) / 3 = 1.67

    Looking at the normal distribution table, the probability corresponding to the z score is 0.953

    Therefore,

    P (x > 109) = 1 - 0.953 = 0.047
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