44. Manufacturing Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing pro

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44. Manufacturing Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed, with a standard deviation of 0.02 mm. (a) What proportion of ball bearings has a diameter more than 5.03 mm

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Thái Dương 5 years 2021-07-21T05:43:47+00:00 1 Answers 26 views 0

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  1. Gerda
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    2021-07-21T05:45:25+00:00
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    Answer:

    0.0668 = 6.68% of ball bearings has a diameter more than 5.03 mm

    Step-by-step explanation:

    When the distribution is normal, we use the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    Manufacturing Ball bearings are manufactured with a mean diameter of 5 millimeters (mm).

    This means that \mu = 5

    With a standard deviation of 0.02 mm.

    This means that \sigma = 0.02

    (a) What proportion of ball bearings has a diameter more than 5.03 mm

    This is 1 subtracted by the pvalue of Z when X = 5.03. So

    Z = \frac{X - \mu}{\sigma}

    Z = \frac{5.03 - 5}{0.02}

    Z = 1.5

    Z = 1.5 has a pvalue of 0.9332

    1 – 0.9332 = 0.0668

    0.0668 = 6.68% of ball bearings has a diameter more than 5.03 mm

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