Week 5. Uniform Distribution

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

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.

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.

For a continuous uniform distribution that ranges from 10 to 20, how many values can be in that range?

• 1

• 11

• 10

• Infinite

• 100

For a continuous probability distribution, the total area under the curve is equal to ____.

An unprincipled used-car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown within the next 6 months. The dealer provides a warranty of 45 days on all cars sold. Let x represent the length of time until the breakdown occurs. Assume that x is a uniform random variable with values between 0 and 6 months.

Calculate the probability that the breakdown occurs while the car is still under warranty (suppose there are 30 days in a month).

• 0.50

• 0.75

• 0.25

• 0.35

Suppose you are given the following function. Can this be an example for a continuous probability distribution?
 $p\left(x\right)\ =\ \frac{1}{2}x,\ \ where\ \ 0\ \le\ x\ \le2.$  

• Yes, because the integral function is different than 1.

• No, because the integral function is different than 1.

• No, because the integral function sums to 1.

• Yes, because the integral function sums to 1.

• I have no idea what you are talking about.

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.

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 standard deviation of the time to resolve the problem? Round your answer to two decimals.

Suppose 8-week old babies' smiling times, in seconds, follow a uniform distribution between zero and 23 seconds.

What is the probability a randomly chosen 8-week-old baby smiles between 2 and 18 seconds?

• 0.62

• 0.70

• 0.76

• 0.78

• 0.50