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

*z-*score for a value of 21.2?**Answer:**1.2To calculate the

*z*-score for a value of*X,*subtract the population mean from*x*and then divide by the standard deviation:What is the

*z-*score for a value of 13.5?**Answer:**–1.0To calculate the

*z-*score 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*z-*score of –0.4?**Answer:**15.6The question gives you a

*z-*score and asks for its corresponding*x-*value. The*z-*formula 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

*z-*formula and then solve for*x:*What value of

*X*corresponds to a*z-*score of 2.2?**Answer:**24.7The question gives you a

*z-*score and asks for its corresponding*x-*value. The*z-*formula 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

*z-*formula and then solve for*x:*

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