The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $100. What is t

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The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $100. What is the z-score for an income of $2,100

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Cora 1 week 2021-09-13T11:19:05+00:00 1 Answer 0

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    2021-09-13T11:20:39+00:00

    Answer:

    The z-score for an income of $2,100 is 1.

    Step-by-step explanation:

    If X \sim N (µ, σ²), then  Z=\frac{x-\mu}{\sigma}, is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z \sim N (0, 1).

    The distribution of these z-variate is known as the standard normal distribution.

    Given:

    µ = $2,000

    σ = $100

    x = $2,100

    Compute the z-score for the raw score x = 2100 as follows:

    Z=\frac{x-\mu}{\sigma}=\frac{2100-2000}{100}=\frac{100}{100}=1

    Thus, the z-score for an income of $2,100 is 1.

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