Understanding Uniform Distribution and Percentiles

This lesson demonstrates how to use Desmos to find percentiles of a uniform distribution. It covers the calculation of the 30th and 75th percentiles for furnace repair times, using the inverse CDF function. The video provides a step-by-step guide to graphing the distribution and verifying results.

What is the range of time a repairman needs to fix a furnace according to the uniform distribution?

• 1 to 4 hours

• 2 to 5 hours

• 1.5 to 4 hours

• 1 to 3 hours

In a uniform distribution, what is the formula for the probability density function?

• f(x) = (b - a) / 1

• f(x) = (a - b) / 1

• f(x) = 1 / (b + a)

• f(x) = 1 / (b - a)

What tool is used to graph the uniform distribution in this lesson?

• Matlab

• Desmos

• Google Sheets

• Excel

What is the 30th percentile of furnace repair times?

• 2.5 hours

• 3 hours

• 2.25 hours

• 1.75 hours

How is the 30th percentile verified in the graph?

• By checking if the area under the curve is 0.9

• By checking if the area under the curve is 0.3

• By checking if the area under the curve is 0.5

• By checking if the area under the curve is 0.7

What percentile represents the longest 25% of repair times?

• 25th percentile

• 75th percentile

• 100th percentile

• 50th percentile

What is the minimum repair time for the longest 25% of repair times?

• 3 hours

• 3.375 hours

• 3.5 hours

• 2.75 hours

How is the 75th percentile verified in the graph?

• By checking if the area to the left is 0.25

• By checking if the area to the left is 0.5

• By checking if the area to the left is 0.75

• By checking if the area to the left is 1

What is the purpose of using the inverse CDF function in this lesson?

• To calculate the mean

• To find the median

• To determine percentiles

• To find the mode

What is the significance of the 75th percentile in this context?

• It represents the most common repair times

• It represents the shortest repair times

• It represents the average repair times

• It represents the longest repair times