The ACT Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 28 and a standard deviation of 4. Assuming these raw scores form a normal distribution:
a) What score separates the lower 45% of the distribution?
b) What number represents the 95th percentile?
c) What is the probability of getting a raw score between 22 and 30?
d) What is the probability of getting a raw score greater than 38?