Finding the z-scores and raw scores

User Generated

yxq887

Mathematics

Description

The following 10 items are based on the following summarized research:

A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5.

Part A**What raw score cuts off the bottom 10.03% of this distribution? Or to phrase another way, what raw score is associated with the 10.03 percentile?


What is the z-score that cuts off the bottom 10.03% of this distribution? Or to phrase another way, what z-score is associated with the 10.03 percentile?  (HINT:  Don't forget that z scores BELOW the mean are negative!)  

What is the raw score that cuts off the bottom 10.03% of this distribution? Or to phrase another way, what raw score is associated with the 10.03 percentile?

Part B**What percentage of the scores is between 57.5 and 65?

Steps:

What is the z-score that corresponds to the raw score of 57.5?

What is the z-score that corresponds to the raw score of 65?

What percentage of the scores is between 57.5 and 65?

Part C:**A raw score of 35 is associated with what percentile?

Steps:

What is the z-score associated with a raw score of 35?

A raw score of 35 is associated with what percentile?

Part D:**What raw scores mark the middle 34% of this distribution? (HINT: DRAW AND SHADE IN THE MIDDLE 34% TO VISUALIZE!  Remember.....the middle 34% means that 17% is BELOW the mean and 17% is ABOVE the mean......)


Steps:

What are the z-scores that mark the middle 34% of this distribution? The z-score below the mean is The z-score above the mean is
What is the raw score below the mean?

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