The distribution of scores on the SAT is approximately normal with a mean of m 5 500 and a standard deviation of s 5100.

For the population of students who have taken the SAT:

a. What proportion have SAT scores less than 400?

b. What proportion have SAT scores greater than 650?

c. What is the minimum SAT score needed to be in the highest 20% of the population?

d. If the state college only accepts students from the top 40% of the SAT distribution, what is the minimum SAT score needed to be accepted?