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 and 40 minutes (100 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 80 and 120 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) =     ,     80 ≤ x ≤ 120  ,     elsewhere (b) What is the probability that the recharge time will be less than 109 minutes?   (c) What is the probability that the recharge time required is at least 91 minutes? (Round your answer to four decimal places.)   (d) What is the probability that the recharge time required is between 90 and 100 minutes?

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!