Question

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability density function for the time it takes to ring up a customer?

Answer 1

Answer:
`f(t)=3.5e^(-3.5 t)\text{ for }t>0`

Explanation:

The probability density function with exponential random variable T(t>0) with mean
`\lambda` is given by :-

`f(t)=\lambda e^(-\lambda t)\text{ for }t>0`

Given : The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes.

i.e.
`\lambda=3.5`

Then , the probability density function for the time it takes to ring up a customer is :

`f(t)=3.5e^(-3.5 t)\text{ for }t>0`