Question

Justin is 22 years old. He spent Friday night out drinking and partying with friends until 3:00 A.M.. Justin lives at home with his parents. His Mom wakes him at 7:00 A.M. Saturday morning because he promised to take her car to the dealer for an oil change and a tire rotation. At the Dealership, Justin is told by the Service Advisor that the job will take about 20 minutes. He is directed to a customer waiting lounge. Justin, however, insists on staying with the car as it goes into the service bay and he ends up getting his way. He wants to catch a quick nap (sleep) in the privacy of the car as he is still feeling the effects of the previous evening. The Service Technician, who will do the work, is a 25 year veteran at the dealership.

Answer 1

The question pertains to high school mathematics, involving the determination of the probability for the time it takes to change car oil, assuming a continuous uniform distribution. The random variable X indicates the time needed, and P(x > 19) calculates to 0.2.

Step-by-step explanation:

The subject of this question is Mathematics, specifically related to the concept of probability and continuous uniform distribution. The grade level would be High School.

a. Write the random variable X in words. X =

The random variable X represents the time needed to change the oil on a car.

b. Write the distribution.

The distribution is a uniform distribution U(11, 21), which means any time between 11 and 21 minutes is equally likely.

c. Graph the distribution.

A graph of this uniform distribution would show a horizontal line from X = 11 to X = 21 with a constant height, indicating an equal probability for any time between those two points. Before X = 11 and after X = 21, the line drops to 0, showing no probability outside of this range.

d. Find P (x > 19).

The probability that the service takes more than 19 minutes is the area under the uniform distribution curve from 19 to 21. Since the entire interval from 11 to 21 represents a length of 10 minutes, each minute has a probability of 1/10. Therefore, P(x > 19) = 2/10 or 0.2.