Question

Problem 97b

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.

In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential.

Step-by-step explanation

Step 1.

As the information in the problem suggests,

  

where

    

Therefore, the mean can be calculated as follows:

The cumulative distribution function for the exponential distribution is given as follows:

  

Required probability can be calculated by,

     

Therefore, the probability that an entire season elapses with a single no-hitter is