Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z

Question

Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between
z
=

1.5
and
z
=
1.5
standard deviations of the mean (or within 1.5 standard deviations of the mean). What percent of the data points will fall in that range?

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Everleigh 3 weeks 2021-11-08T15:28:55+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-08T15:30:26+00:00

    Answer:

    86.64% of the data points will fall in that range

    Step-by-step explanation:

    Problems of normally distributed samples are solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

    In this problem:

    z = -1.5 has a pvalue of 0.0668

    z = 1.5 has a pvalue of 0.9332

    0.9332 – 0.0668 = 0.8664

    86.64% of the data points will fall in that range

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