The instructor of a class announces that the numerical score in a midterm test,
approximated as a real number, has a triangular density function spread be-
tween 30 and 95. The density function peaks at 80, and a score of 7 0 is a pass.
A st udent only knows his/her performance in terms of a pass/fail result. At the
end of the semester, the top 10% of the students are awarded a scholarship.
(a) Determine the peak value of the density function.
(b) Determine the mean and variance of the score.
(c) G iven that a student passed, what is the probability that he/she will be
awarded a scholarship?