Z scores

On the assumption that IQ's are normally distributed in the population with a mean of 100 and a standard deviation of 15, answer the following questions:

a. What percentage of the population has an IQ above 135?

b. If n=20,000, how many people would have an IQ above 90?

c. What would be the IQ such that 30% of the scores are below it?

d. What would be the IQ of a genius if a genius is defined as someone whose IQ is at the top 2% of the population?

A teacher decided to fail 12% of her class of 40 students. The exam results of the class were roughly normally distributed with a mean of 74 and a standard deviation of 7.

a. What score must a student get in order to pass?

b. How many students would get a score between 77 and 85?