Question

The electric-vehicle manufacturing company Tesla estimates that a driver who commutes miles per day in a Model S will require a nightly charge time of around hour and minutes ( minutes) to recharge the vehicle's battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between and minutes.
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 than 110 minutes?C. What is the probability that the recharge time required is at least 100 minutes?D. What is the probability that the recharge time required is between 95 and 110 minutes?

Answer 1

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Please find the complete question in the attached file.

In this question, we assume that "x" denotes as  an actual time of the  battery charging, that is a uniform random variable that $x \sim U(90, 120)$

 In point a:

so, pdf of x =

$\to f(x)= \frac{1}{120-90} = \frac{1}{30} \\\\\to 90 < x$

In point b:

To find

$\to P(x$

In point c:

$\to P(x$

In point d:

$\to P(95< x< 110)$

$= \int^{110}_{95} \frac{1}{30} \ dx\\\\= \frac{110-95}{30} \\\\= \frac{15}{30} \\\\= \frac{1}{2}$