The test scores in a statistics course are normally distributed with a mean of 77 points and a standard deviation of 13 points. Show your work to answer the following.
a. Students need a score of 60 points to pass the exam. What is the probability that a randomly selected student will pas the exam? (P(X ≥ 60))
b. If 560 students take the exam, how many should be expected to pass (X ≥ 60) the exam?
c. What percentage of students earn an 'A' on the exam? (Students need a score of 90 points or better to earn an 'A'.)
d. If the instructor wants to assign the top 20% of her class a grade of 'A', then what score do the students need to earn an 'A'?