Scores on a standardized test form a normal distribution with = 500 with = 100.

a. What percentage of scores lie below X = 340?

b. What percentage of scores lie are higher than X= 578?

c. What percentage of scores lie between 567 and 746?

d. What percentage of scores lie between 290 and 467?

e. What percentage of scores lie between 290 and 746?

f. If the state college only accepts students who score in the top 80% on the SAT, what is the minimum score needed to be accepted?

g. If the state college only accepts students who score in the top 10% on the SAT, what is the minimum score needed to be accepted?