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

For a normal distribution, the z-score for an income of $2,100 is 1

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

Given that:

μ = $2000, σ = $100. For x = $2100:

For a normal distribution, the z-score for an income of $2,100 is 1

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

Step-by-step explanation:

If X N (µ, σ²), then  , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z 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:

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

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

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step-by-step explanation: