1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

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1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

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Neala 3 years 2021-07-22T10:33:26+00:00 1 Answers 6 views 0

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  1. Helga
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    2021-07-22T10:35:13+00:00
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    Answer:

    0.6826 = 68.26% probability that you have values in this interval.

    Step-by-step explanation:

    Normal Probability Distribution

    Problems of normal distributions can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

    X~N(8, 1.5)

    This means that \mu = 8, \sigma = 1.5

    What is the probability that you have values between (6.5, 9.5)?

    This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So

    X = 9.5

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

    Z = \frac{9.5 - 8}{1.5}

    Z = 1

    Z = 1 has a p-value of 0.8413.

    X = 6.5

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

    Z = \frac{6.5 - 8}{1.5}

    Z = -1

    Z = -1 has a p-value of 0.1587

    0.8413 – 0.1587 = 0.6826

    0.6826 = 68.26% probability that you have values in this interval.

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