A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 127 with standard deviation of 22, and the mean length of

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A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 127 with standard deviation of 22, and the mean length of two-year-old spotted flounder is 158 with a standard deviation of 23. The distribution of flounder lengths is approximately bell-shaped. Part 1 of 4 (a) Anna caught a one-year-old flounder that was 155 millimeters in length. What is the z-score for this length

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Amity 4 years 2021-08-07T18:12:46+00:00 1 Answers 22 views 0

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  1. bonexptip
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    2021-08-07T18:14:01+00:00
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    Answer:

    The z-score for this length is of 1.27.

    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.

    One-year-old flounder:

    Mean of 127 with standard deviation of 22, which means that \mu = 127, \sigma = 22

    Anna caught a one-year-old flounder that was 155 millimeters in length. What is the z-score for this length

    This is Z when X = 155. So

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

    Z = \frac{155 - 127}{22}

    Z = 1.27

    The z-score for this length is of 1.27.

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