Uniform Distribution and Repair Times

The video tutorial explains the concept of uniform distribution, particularly in the context of repair times for furnaces, which range from 1.5 to 4 hours. It introduces the probability density function and demonstrates how to calculate probabilities for different time intervals using both Desmos graphing tools and manual calculations. The tutorial covers finding probabilities for repair times greater than two hours, less than three hours, and between two and three hours, emphasizing the use of area under the curve for these calculations.

What is the range of repair times for the furnace in the given problem?

• 0.5 to 3.5 hours

• 2 to 3 hours

• 1.5 to 4 hours

• 1 to 5 hours

What is the probability density function value for the uniform distribution in this problem?

• 0.6

• 0.4

• 0.2

• 0.5

How do you calculate the probability that a repair takes more than 2 hours?

• By finding the area under the curve from 3 to 4

• By finding the area under the curve from 2 to 4

• By finding the area under the curve from 1.5 to 4

• By finding the area under the curve from 1.5 to 2

Which tool is used to graph the uniform distribution in this tutorial?

• Google Sheets

• Excel

• Desmos

• Matplotlib

What is the probability that a repair takes more than 2 hours?

• 0.7

• 0.9

• 0.6

• 0.8

How is the probability of a repair taking less than 3 hours calculated manually?

• By multiplying the base of 3 by the height of 0.4

• By multiplying the base of 2.5 by the height of 0.4

• By multiplying the base of 1.5 by the height of 0.4

• By multiplying the base of 1 by the height of 0.4

What is the probability that a repair takes less than 3 hours?

• 0.5

• 0.6

• 0.7

• 0.8

What is the probability that a repair takes between 2 and 3 hours?

• 0.5

• 0.4

• 0.3

• 0.2

How is the probability of a repair taking between 2 and 3 hours calculated manually?

• By multiplying the base of 2 by the height of 0.4

• By multiplying the base of 1.5 by the height of 0.4

• By multiplying the base of 0.5 by the height of 0.4

• By multiplying the base of 1 by the height of 0.4

What is the height of the probability density function in this uniform distribution?

• 0.4

• 0.6

• 0.3

• 0.5