# [Solution]Standard Normal Probability Distribution (z-scores)

Chapter 6 Part 2: Standard Normal Probability Distribution (z-scores) Assume that you have a normal distribution of IQ scores with a mean of 100 and…

Chapter 6 Part 2: Standard Normal Probability Distribution (z-scores)

Assume that you have a normal distribution of IQ scores with a mean of 100 and a standard deviation of 10.

What is the z-score for a raw score of 115?
What is the z-score for a raw score of 83?
What is the z-score for a raw score of 70?
What is the area between the mean and the z-score of 115?
What is the area beyond the mean the z-score 70?
What proportion of a cases have an IQ score above 115?
What proportion of cases have an IQ score between 90 and 110?

You became privy to the issue of mass incarceration in the United States during your college studies and wish to reduce the overreliance on prisons. As a correctional officer, you are allowed to implement a rehabilitation program in your prison that may help current inmates be released early. The Warden stipulates that only those who score in the top 5% of a post-treatment assessment test will be considered for early release. The mean of this test is 75, and the standard deviation is 15.

Would a person with a raw score of 85 be accepted?
Would a person with a raw score of 98 be accepted?
What is the minimum score you would have to have on the test to be accepted?

What z scores fall until the lower .24 of the distribution?

What z score fall into the upper .39 of the distribution?

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