In 1994, Charles Murray and Richard Herrnstein published a book titled The Bell Curve where they proposed a robust link between intelligence and crime where intelligence decreases crime increases. Since then, it has been heavily critiqued both theoretically and methodologically. 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 proportion of the cases has an IQ score above 115?
• What proportion of the cases has an IQ score between 90 and 110?
• What is the probability that you would find an IQ score of 70 or below?
• What is the probability that you would find an IQ score of 125 or above?

I have the first three, and they are:

1. 1.5

2. 1.7

3. -.30

However, I do not understand how to get the answers for the next four portions of the question. I would like to understand the equations used to solve the problems step by step, if possible, please.