Question

Suppose the waiting time in a Piggly Wiggly checkout line follows an Exponential distribution with an average wait of 7 minutes. What is the 80th percentile of waiting times?

Answer 1

Answer: 11.3 minutes

Step-by-step explanation: Exponential Distribution is a distribution with function of the form:

$f(x)=\lambda.e^{-\lambda.x}$

often related to an amount of time until an event occur.

The greek letter λ is decay parameter and have a relationship with the mean:

$\lambda=\frac{1}{\mu}$

and x is the amount of time

Probability in exponential distribution is given by

$P(x<X)=1-e^{-\lambda.x}$

Percentile is a value below which a percentage of the data falls.

For the waiting line in a Piggly Wiggly checkout, 80th percentile will be

$P(x<h)=0.8$

$P(x<h)=1-e^{-\frac{1}{7}h}$

$0.8=1-e^{-\frac{1}{7}h}$

$e^{-\frac{h}{7} }=0.2$

$-\frac{h}{7} =ln(0.2)$

h = 11.3

The 80th percentile of waiting times is 11.3 minutes.