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18 January, 22:17

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 111 cm and a standard deviation of 5.2 cm. A. Find the probability that one selected subcomponent is longer than 113 cm.

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  1. 18 January, 22:46
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    Answer: the probability that one selected subcomponent is longer than 113 cm is 0.65

    Step-by-step explanation:

    if the lengths of an important subcomponent are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = lengths of selected subcomponent.

    µ = mean length

    σ = standard deviation

    From the information given,

    µ = 111 cm

    σ = 5.2 cm

    We want to find the probability that one selected subcomponent is longer than 113 cm. It is expressed as

    P (x > 113) = 1 - P (x ≤ 113)

    For x = 113,

    z = (113 - 111) / 5.2 = - 0.38

    Looking at the normal distribution table, the probability corresponding to the z score is 0.35

    P (x > 113) = 1 - 0.35 = 0.65
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