Posts Tagged ‘z- Score’

Problem 650

The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-Score for a student who finishes the test in 45 minutes?

 

Solution:-

 

z = \frac{(45 - 60)}{10}

z =\frac{ -15}{10}

z = -1.5

 

z- Score

z- Score

If a normal distribution has mean µ and standard deviation \sigma, then the z-score for the number x is

z = \frac{x-\mu }{\sigma }.

 

Example:- If a normal distribution has mean 50 and standard deviation 4, find the following

z-scores. The z-score for x= 46

 

Solution :- Since 46 is 4 units below 50 and the standard deviation is 4, 46 is

1 standard deviation below the mean. So, its z-score is -1.