Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness o

Question

Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2731 mm with a standard deviation of 0.000959 mm.

a. A certain shipment has a diameter of 0.2761. Find the standardized: score of the shipment.
b. Is this an outerlier?

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Mary 2 weeks 2021-09-14T08:18:33+00:00 1 Answer 0

Answers ( )

    0
    2021-09-14T08:20:26+00:00

    Answer:

    a) 3.128

    b) Yes, it is an outerlier

    Step-by-step explanation:

    The standardized z-score for a particular sample can be determined via the following expression:

    z_i = {x_i -\bar x}/{s}

    Where;

    \bar x = sample means

    s = sample standard deviation

    Given data:

    the mean shipment thickness (\bar x) = 0.2731 mm

    With the standardized deviation (s) = 0.000959 mm

    The standardized z-score for a certain shipment with a diameter x_i= 0.2761 mm can be determined via the following previous expression

    z_i = {x_i -\bar x}/{s}

    z_i = {0.2761-0.2731}/{ 0.000959}

    z_i = 3.128

    b)

    From the standardized z-score

    If [z_i < 2]; it typically implies that the data is unusual

    If [z_i > 2]; it means that the data value is an outerlier

    However, since our z_i > 3 (I.e it is 3.128), we conclude that it is an outerlier.

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