Question

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 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes.
(a)
Give a mathematical expression for the probability density function of battery recharging time for this scenario.
f(x) =

, 70 ≤ x ≤ 110
, elsewhere

Answer 1

Using the uniform distribution, it is found that the mathematical expression for the probability density function of battery recharging time for this scenario is given by:

$f(x) = \frac{1}{40}, 70 \leq x \leq 110$

$f(x) = 0$, elsewhere.

What is the uniform probability distribution?

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability density function is:

$f(x) = \frac{1}{b - a}, a \leq x \leq b$

$f(x) = 0$, elsewhere.

In this problem, the actual recharging time required is uniformly distributed between 70 and 110 minutes, hence a = 70, b = 110, and the density function is:

$f(x) = \frac{1}{40}, 70 \leq x \leq 110$

$f(x) = 0$, elsewhere.

More can be learned about the uniform distribution at https://brainly.com/question/13889040