Normal Distribution

Question

Heights of adult women in the United States are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. A medical researcher is planning to select a large random sample of adult women to participate in a future study. What is the standard value, or z-value, for an adult woman who has a height of 68.5 inches?

Answer 1

 

Hi James,

 

In case of a normal distribution,

 

a standard/normalized value can be obtained according to the following formula

 

     z = (Z - μ)/σ

 

where Z is a sample value to be normalized.

 

In this problem, as Z = 68.5

 

     z = (68.5 - 63.5)/2.5

 

        = 5.0/2.5

 

        = 2.0