The length of time it takes students to complete a statistics examination is uniformly distributed and varies between35and60minutes.

(a) Find the mathematical expression for the probability density function.

f(x) = ( ?/0 , 35x60

elsewhere

(b)Compute the probability that a student will take between40and45minutes to complete the examination.

(c)Compute the probability that a student will take no more than35minutes to complete the examination.

(d)What is the expected amount of time (in min) it takes a student to complete the examination? min

(e)What is the variance for the amount of time it takes a student to complete the examination? (Round your answer to two decimal places.)