The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the proportion

Question

The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the proportion of flanges that exceeds 0.99 millimeters.

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Eirian 4 years 2021-08-14T21:59:15+00:00 1 Answers 29 views 0

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  1. thienan
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    2021-08-14T22:01:11+00:00
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    Answer:

    The proportion of flanges that exceeds 0.99 millimeters is 0.6

    Explanation:

    Given;

    integral range of [0.95,  1.05]

    Let X be a variable with uniform distribution over the given range.

    Then, f(x) = \frac{1}{1.05 -0.95} =10

    1 – 0.95 = 0.05, 1.05 – 1 = 0.05

    \ minimum, f_(x) = \frac{0.05}{1.05 -0.95} =0.5\\\\

    interval = 10 – 0.5 = 9.5

    F(x) = 10x + 9.5

    When, X exceeds 0.99 millimeters, then the proportion of flanges will be;

    P (X > x) = 1 – F(x)

    P( X > 0.99 ) = 1 – 10(0.99) + 9.5

    P( X > 0.99 ) = 0.6

    Therefore, the proportion of flanges that exceeds 0.99 millimeters is 0.6

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