z  Statistic 



Objectives:
By the end of this lesson, you should be able to: 
1. Determine the zscore given a mean and standard deviation, and vice versa.  
The z statistic has a normal distribution with a mean of zero and a standard deviation of one. Therefore, if we know the mean and standard deviation for a population, we can identify a zscore given the raw score, or we can identify the raw score given the zscore.Example 1: A parts manufacturer produces a framis. The framis has a mean weight of 8 pounds, with a standard deviation of 2 ounces. You measure one particular framis and find it weighs 8 pounds, three ounces. What is its zscore?Example 2: The boss then asks you to reject all but the middle 90% of the framises. Where do you establish the minimum and maximum acceptable weights? Use a table that shows the area under the normal curve, such as the one at:Test your knowledge: 3. Using the table under the normal curve, calculate the percentile score of a student who scores 490 on a test that has a mean of 460 and a standard deviation of 40. 



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© Jim Flowers Department of Technology, Ball State University 