High School

The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable [tex]X[/tex] having the density function given in exercise 4.15 on page 114. Find the variance of [tex]X[/tex].

A. Not enough information
B. 5000 hours
C. 10000 hours
D. 250000 hours

Answer :

Final answer:

The random variable X represents the time needed to change the oil in a car, which follows a uniform distribution. The probability that the time needed is greater than 19 minutes is 0.2.

Explanation:

a. The random variable X represents the amount of time a service technician needs to change the oil in a car.

b. The random variable X follows a uniform distribution.

c. The graph of the distribution would be a rectangle with a base between 11 and 21 and a height of 1/(21-11) = 1/10.

d. To find P(x > 19), we need to find the area under the distribution curve that corresponds to values greater than 19. Since the distribution is uniform, the area is given by (21-19) * (1/(21-11)) = 2/10 = 0.2.

Learn more about Uniform distribution here:

https://brainly.com/question/10999921

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