Use the following information to answer the next three exercises. The average lifetime of a certain new smartphone is three years. The manufacturer will replace any smartphone failing within two years of the date of purchase. The lifetime of these smartphones 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.
- What is the probability that an entire season elapses with a single no-hitter?
- If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season?
- What is the probability that there are more than 3 no-hitters in a single season?
OpenStax Introductory Statistics 2e, 5.3 The Exponential Distribution, exercise 55