Question

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

Answer 1

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.