Answer all parts: Exam marks are Normally distributed with mean 65% and a standard deviation of 5%. (a) Find the probability that a student will score more than 60% on the exam. (b) What percent of...

Answer all parts:

Exam marks are Normally distributed with mean 65% and a standard deviation of 5%.
(a) Find the probability that a student will score more than 60% on the exam.
(b) What percent of students score between 70% and 90% on the exam?
(c) If you want to score in the top 5% of all students, what minimum mark would you have to earn on the exam?
(d) What is the median mark on the exam?
(e) Which mark will be scored by the most number of students?
(f) Suppose you keep randomly sampling students until you find a student who has scored more than 60% on the exam. You have sampled more than 10 students so far and they have all scored 60% or less. What is the probability that you will have to sample more than 15 students in total?
(g) Suppose you keep randomly sampling students until you find 3 students who have scored more than 60% on the exam. On average, how many students in total will you have to sample?