Question: Scores on an examination taken by a large group of students are normally distributed with mean 700 and standard deviation 120.

(a) An A is awarded for a score higher than 820. What proportion of students will obtain an A?

(b) It is decided to give a failing grade to 5% of the students with the lowest grade. What is the minimum score necessary to pass this exam?

(c) A sample of five students is taken at random. What is the probability that at least four will pass the exam? What is the expected number of students that will pass the exam.