The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.

Question

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random will be less than 29.75 inches long

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Madeline 3 weeks 2021-12-28T22:40:55+00:00 1 Answer 0 views 0

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    2021-12-28T22:42:45+00:00

    Answer:

    6.68% or 0.0668

    Step-by-step explanation:

    Mean sheet length (μ) = 30.05 inches

    Standard deviation (σ) = 0.2 inches

    In a normal distribution, for any length X, the z-score is determined by the following expression:

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

    For X = 29.75, the z-score is:

    z=\frac{29.75-30.05}{0.2}\\z=-1.5

    A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution.

    Therefore, the probability that a sheet selected at random will be less than 29.75 inches long is 6.68%.

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