Question

The average time in minutes to get your car inspected with the Division of Motor Vehicles is 50 minutes. Assume you arrive just as another car begins the inspection process. However, you need to be done and on the road in 30 minutes or less to pick-up your children from school. You decide to get the car inspected at this time. What is the probability you are on time to pick-up your children

Answer 1

45.12%

Explanation:

We have that l = 50

The probability density function of the exponential distribution is:

(1 / l) * e ^ (x * 1 / l) l> 0

f (X = x) = 0 otherwise

in this case X would come being the probability the road in 30 minutes or less to pick-up the children to go to school, it would come being:

P (X <= 30) = integral from 0 to 30 [1/50 e ^ (x / 50) dx]

It is integral as a result:

P (X <= 30) = (1/50) [e ^ (- x / 50) / (-1/50)]

We evaluate x = 0 up to x = 30

P (X <= 30) = (1/50) [e ^ (- 30/50) / (-1/50)] - (1/50) [e ^ (- 0/50) / (-1 / fifty)]

P (X <= 30) = -0.5488 - (-1)

P (X <= 30) = 0.4512

Therefore the probability is 45.12%