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10 April, 23:03

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 2 inches. assume the variable x is normally distributed. left parenthesis a right parenthesis what percent of the fish are longer than 12? inches

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  1. 11 April, 03:01
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    To solve this problem, we make use of the z statistic. What we have to do here is to find for the z score using the given data and from the standard probability tables for z, we locate the proportion of the fish longer than 12 inches.

    The formula for calculating the z score is:

    z = (x - μ) / σ

    where,

    x = the sample value = 12 inches

    μ = the sample mean = 11 inches

    σ = 2 inches

    so,

    z = (12 - 11) / 2

    z = 1 / 2

    z = 0.5

    Since we are looking for the values greater than 12, so this is a right tailed test. Using the tables, the value of p at this value of z is:

    p (z = 0.5) = 0.3085

    Therefore there is a 30.85% probability that the fish is longer than 12 inches.
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