Please help ASAP

On a recent statewide math test, the raw score average was 56 points with a standard deviation of 18. If the scores were normally distributed and 24,000 students took the test, answer the following questions.

A. If the state would like to scale the test so that a 90% would correspond to a raw score that is one and a half standard deviations above the mean, what raw score is needed for a 90%?

B. How many of the 24,000 students receive a scaled score greater than a 90%?

Please help explain this I'm very confused.

Question

Please help ASAP

On a recent statewide math test, the raw score average was 56 points with a standard deviation of 18. If the scores were normally distributed and 24,000 students took the test, answer the following questions.

A. If the state would like to scale the test so that a 90% would correspond to a raw score that is one and a half standard deviations above the mean, what raw score is needed for a 90%?

B. How many of the 24,000 students receive a scaled score greater than a 90%?

Please help explain this I'm very confused.

angel_kitty12 · Answer

Also with these two problems that connect to this question.

D. The state would like no more than 550 of the 24,000 students to fail the exam. What percent of the total does the 550 represent? Round to the nearest tenth of a percent.

E. What would the raw passing score be set at so that no more than the 550 students fail?

I thought I understood these but I don't. Please help!!