Scores on an examination taken by a very 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 all students obtain an A?

(b) A B is awarded for scores between 730 and 820.

An instructor has a section of 100 students, who can be viewed as a random sample of all students in the large group. Find the expected number of students in this section who will obtain a B.

(c) It is decided to give a failing grade to the 5% of students with the lowest scores. What is the minimum score needed to avoid a failing grade?