Question

Problem 96a

Answer 1

Given information

Use the following information to answer the next three exercises. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

At a  call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has an exponential distribution.

Step-by-step explanation

Step 1.

As given in the problem that the average lifetime of a certain new cell phone is three years. And the manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

Therefore,

 

where

 

The decay rate is given by

  

On average one call is received in two minutes, therefore five calls will be received in

.