A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The

Question

A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablets varies a bit, with the N(11.7, 0.3) distribution. The process specifications call for applying a force between 11.5 and 12.5 kg.

(a) What percent of tablets are subject to a force that meets the specifications?
(b) The manufacturer adjusts the process so that the mean force is at the center of the specifications, mu = 11.8 kg. The standard deviation remains 0.2 kg. What percent now meet the specifications?

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bonexptip 2 months 2021-07-29T23:19:43+00:00 1 Answers 1 views 0

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    2021-07-29T23:21:05+00:00

    Answer:

    a) 74.5%

    b) 93.3%

    Explanation:

    μ = 11.7

    σ = 0.3

    standardize x to z = (x – μ) / σ

    P( 11.5 < x < 12.5) =

    P[( 11.5 – 11.7) / 0.2 < Z < ( 12.5 – 11.7) / 0.3] =

    P( -0.67 < Z < 2.67) =

    0.9962 – 0.2514 =

    0.7448 = 74.5%

    (From Normal probability table)

    b)

    μ = 11.8

    σ = 0.2

    standardize x to z = (x – μ) / σ

    P( 11.5 < x < 12.5) =

    P[( 11.5 – 11.8) / 0.2 < Z < ( 12.5 – 11.8) / 0.2]

    P( -1.5 < Z < 3.5) =

    0.9999 – 0.0668 =

    0.9333 = 93.3%

    (From Normal probability table)

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