Problem 96d
Page 331
Section: Homework
Chapter 5: CONTINUOUS RANDOM VARIABLES
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.
Step-by-step explanation
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
The cumulative distribution function for the exponential distribution is given as follows:
Required probability can be calculated by,
Therefore, the probability that the next call will occur within the next minute is
.