# 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?