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# A psychologist studied self esteem scores and found the data set to be normally distributed with…

A psychologist studied self-esteem scores and found the data set to be normally distributed with a mean of 50 and a standard deviation of 6.

Part A**What raw score cuts off the bottom 33% of this distribution?

Steps:

Q1: What is the z-score that cuts off the bottom 33% of this distribution?

Q2: What is the raw score that cuts off the bottom 33% of this distribution?

Part B**What percentage of the scores is between 56 and 62?

Steps:

Q3: What is the z-score that corresponds to the raw score of 56?

Q4: What is the z-score that corresponds to the raw score of 62?

Q5: What percentage of the scores is between 56 and 62?

Part C:**A raw score of 47 is associated with what percentile?

Steps:

Q6: What is the z-score associated with a raw score of 47?

Q7: A raw score of 47 is associated with what percentile?

Part D:**What raw scores mark the middle 95% of this distribution?

Steps:

Q8: What are the z-scores that mark the middle 95% of this distribution?

Q9: What is the raw score below the mean?

Q10: What is the raw score above the mean?

Part E:**What is the median of this distribution?

Q11: What is the median of this distribution?