Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and40minutes (100minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between85and115minutes.

(a)

Give a mathematical expression for the probability density function of battery recharging time for this scenario.

(b)

What is the probability that the recharge time will be less than108minutes?

(c)

What is the probability that the recharge time required is at least92minutes?

(d)

What is the probability that the recharge time required is between90and105minutes?