# Finding the z-scores and raw scores

**Question 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 is the raw score below the mean?

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