A professor uses a relative scale for grading. She announces that 60% of the students will get at least a B, with 15% getting A’s. Also, 5% will get a D and another 5% will get an F. Assume that no incompletes are given in the course. Let Score be defined by 4 for A, 3 for B, 2 for C, 1 for D, and 0 for F.

a. Find the probability that a student gets a B.

b. Find the probability that a student gets at least a C.

c. Compute the expected value and the standard deviation of Score.