Finding the z-scores and raw scores

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!)   Blank 1

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? Blank 2

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? Blank 3

What is the z-score that corresponds to the raw score of 65? Blank 4

What percentage of the scores is between 57.5 and 65? Blank 5

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? Blank 6

A raw score of 35 is associated with what percentile? Blank 7

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 Blank 8 The z-score above the mean is Blank 9
What is the raw score below the mean? Blank 10