Understanding Uniform Distribution with Desmos

The video tutorial demonstrates how to determine the mean and standard deviation of a uniform distribution using Desmos.com. It uses a practical example of a repairman's time to fix a furnace, which is uniformly distributed between 1.5 and 4 hours. The tutorial guides viewers through graphing the distribution on Desmos, calculating the mean and standard deviation, and verifying these calculations. The mean is found to be 2.75 hours, and the standard deviation is approximately 0.7217. The video concludes with a verification of these results using both Desmos and formulaic calculations.

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

• 1.5 to 4 hours

• 2 to 5 hours

• 1 to 5 hours

• 0.5 to 4 hours

How is the probability density function for a uniform distribution defined?

• f(x) = (b + a) / 1

• f(x) = 1 / (b - a)

• f(x) = (b - a) / 1

• f(x) = 1 / (b + a)

What is the probability density function value for the given uniform distribution?

• 0.2

• 0.4

• 0.5

• 0.6

What is the purpose of graphing the uniform distribution in Desmos?

• To calculate the range

• To find the standard deviation only

• To visualize the distribution and find cumulative probability

• To find the mean only

What is the mean repair time calculated using Desmos?

• 2.75 hours

• 3.25 hours

• 3 hours

• 2.5 hours

Where does the mean value lie in a uniform distribution?

• Outside the range

• At the beginning

• In the middle

• At the end

What is the standard deviation of the repair time as calculated using Desmos?

• 1.0217

• 0.8217

• 0.7217

• 0.9217

Which function in Desmos is used to calculate the standard deviation?

• mode

• mean

• variance

• stdev

What is the significance of the standard deviation in a distribution?

• It indicates the spread of data

• It shows the average value

• It calculates the median

• It determines the range

How does the calculated standard deviation using Desmos compare to the formula?

• It is not comparable

• It is approximately the same

• It is slightly different

• It is significantly different