Working with zScores and Values of X
The practice problems here will help you understand the standard normal (Z) distribution, its properties, and how its values are interpreted and used. In the problems below, the random variable X has a normal distribution, with a mean of 17 and a standard deviation of 3.5.
Sample questions

What is the zscore for a value of 21.2?
Answer: 1.2
To calculate the zscore for a value of X, subtract the population mean from x and then divide by the standard deviation:

What is the zscore for a value of 13.5?
Answer: –1.0
To calculate the zscore for a value of X, subtract the population mean from x and then divide by the standard deviation:

What value of X corresponds to a zscore of –0.4?
Answer: 15.6
The question gives you a zscore and asks for its corresponding xvalue. The zformula contains both x and z, so as long as you know one of them you can always find the other:
You know that z = –0.4,
and
so you just plug these numbers into the zformula and then solve for x:

What value of X corresponds to a zscore of 2.2?
Answer: 24.7
The question gives you a zscore and asks for its corresponding xvalue. The zformula contains both x and z, so as long as you know one of them you can always find the other:
You know that z = 2.2,
and
so you just plug these numbers into the zformula and then solve for x:
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