Understanding Percentiles in Exponential Distribution

The video tutorial explains how to find the 70th percentile of an exponential distribution. It begins by introducing the problem, where a postal clerk's service time follows an exponential distribution with a mean of four minutes. The tutorial covers the probability density function (PDF) and cumulative distribution function (CDF) for this distribution. It then demonstrates how to solve for the 70th percentile using the CDF and logarithmic transformations. Finally, a shortcut formula for calculating percentiles is introduced and verified.

What is the mean time a postal clerk spends with a customer in this example?

• 4 minutes

• 3 minutes

• 2 minutes

• 5 minutes

What is the decay parameter (m) for the exponential distribution in this example?

• 0.25

• 1.0

• 0.75

• 0.5

What does the cumulative distribution function (CDF) represent in this context?

• The average value of x

• The probability of x being less than or equal to a value

• The probability of x being greater than a value

• The maximum value of x

In the context of this problem, what does the 70th percentile represent?

• 70% of customers take exactly this time

• 70% of customers take more than this time

• 70% of customers take twice this time

• 70% of customers take less than or equal to this time

What is the first step in solving the equation for the 70th percentile?

• Add 1 to both sides

• Divide both sides by 0.3

• Multiply both sides by 0.25

• Subtract 1 from both sides

What is the approximate value of k, the 70th percentile, in this example?

• 3.5 minutes

• 4.0 minutes

• 4.8 minutes

• 4.5 minutes

What mathematical operation is used to solve the exponential equation for k?

• Multiplication

• Logarithm

• Subtraction

• Addition

What is the base of the logarithm used in solving for k?

• 2

• e

• 10

• 5

What is the advantage of using the shortcut formula to find the percentile?

• It is more accurate

• It provides a different result

• It requires no calculations

• It is faster

What is the formula used to find the 70th percentile using the shortcut method?

• Natural log of 0.7 divided by 0.25

• Natural log of 0.3 divided by -0.25

• Natural log of 1.3 divided by 0.25

• Natural log of 0.3 divided by 0.25