Education professionals refer to science, technology, engineering and mathematics as the STEM disciplines. A recent ACT Condition and Career Readiness Report states that 47% of high school graduates have expressed interest in a STEM discipline. A random sample of 85 freshmen is selected.

a. Is it appropriate to use the normal approximation to find the probability that less than 45% of the freshmen in the sample have expressed interest in a STEM discipline? If so, find the probability. If not, explain why not.

b. A new sample of 150 freshmen is selected. Find the probability that less than 45% of the freshmen in this sample have expressed interest in a STEM discipline.

c. Find the probability that the proportion of freshmen in the sample of 150 who have expressed interest in a STEM discipline is between 0.40 and 0.45.

d. Find the probability that more than 38% of the freshmen in the sample of 150 have expressed interest in a STEM discipline.

e. Would it be unusual if less than 42% of the freshmen in the sample of 150 have expressed interest in a STEM discipline?