Continuous Uniform Distribution

The number of miles driven by a truck driver falls between 300 and 700 and follows a uniform distribution.

Calculate the 90th percentile of the number of miles driven by a truck driver.

(leave the unit out when writing the answer)

If X is a uniformly distributed random variable that has probability density function f(x) in the interval [6, 17], what is c in the above diagram?

• 11

Customers experiencing technical difficulty with their Internet cable service may call for technical support. It takes the technician between 2 minutes and 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

What percent of the problems take more than 5 minutes to resolve? Provide your answer in decimal form. Do not include the percentage sign.

Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and four hours. Let x = the time needed to fix a furnace.

Find the 30th percentile of furnace repair times. Round your answer to two decimals.

Suppose the time it takes a nine-year-old to eat a doughnut is between 0.5 and 4 minutes, inclusive. Let X = the time, in minutes, it takes a nine-year-old child to eat a doughnut, find the probability that a randomly selected nine-year-old child eats a doughnut in at least two minutes. give your answer to 3 decimal places.

Suppose that the value of stock varies each day from $16 to $25 with a uniform distribution. Find the probability that the value of the stock is more than $19.

give your answer to 3 decimal places.

Suppose that the value of stock varies each day from $16 to $25 with a uniform distribution. Given that the stock is greater than $18, find the probability that the stock is more than $21.

give your answer to 3 decimal places.

The continuous random variable X has p.d.f as shown in the diagram.

What are the values of a and b for the probability function?

• a = 5.5

  b = 3.5

• a = 3.5

  b = 5.5

• a = 5.5

  b = 0.5

• a = 0.5

  b = 3.5

Customers experiencing technical difficulty with their Internet cable service may call for technical support. It takes the technician between 2 minutes and 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

What is the mean time to resolve the problem?

• 5 minutes

• 6 minutes

• 4 minutes

• 3 minutes

Many retail stores offer their own credit cards. At the time of the credit application, the customer is given a 10% discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.

What is the likelihood a particular application will take less than 6 minutes? Round your answer to two decimal places.