Answer:
The z-score for an income of $2,100 is 1.
Step-by-step explanation:
If X [tex]\sim[/tex] N (µ, σ²), then [tex]Z=\frac{x-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] 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:
[tex]Z=\frac{x-\mu}{\sigma}=\frac{2100-2000}{100}=\frac{100}{100}=1[/tex]
Thus, the z-score for an income of $2,100 is 1.
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:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score, \mu=mean,\sigma=standard \ deviation[/tex]
Given that:
μ = $2000, σ = $100. For x = $2100:
[tex]z=\frac{x-\mu}{\sigma} \\\\z=\frac{2100-200}{100} \\\\z=1[/tex]
For a normal distribution, the z-score for an income of $2,100 is 1
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