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24 August, 06:16

Suppose the length of an oarfish is normally distributed with a mean of 6.5 m and a standard deviation of 1.5 m. Which group describes 16% of the oarfish population? Select each correct answer. oarfish that are between 6.5 m and 9.5 m oarfish that are shorter than 5 m oarfish that are between 3.5 m and 9.5 m oarfish that are longer than 8 m

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  1. 24 August, 08:15
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    Step-by-step explanation:

    Let x be the random variable representing the length of an oarfish. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

    z = (x - µ) / σ

    Where

    x = sample mean

    µ = population mean

    σ = standard deviation

    The given probability value is 16% = 0.16. From the normal distribution table, the z score corresponding to the probability value is - 0.99

    This indicates that the sample mean is lower than the population mean

    Therefore,

    - 0.99 = (x - 6.5) / 1.5

    - 0.99 * 1.5 = x - 6.5

    - 1.5 = x - 6.5

    x = - 1.5 + 6.5

    x = 5m

    The correct answer is

    oarfish that are shorter than 5 m
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