MATH 314 Homework 05

1. Consider a busy intersection in a city. Past data has shown that, on average, 5 vehicles per hour make a wrong turn at this intersection due to a lack of clear signage.
   1. What is the probability that exactly 3 vehicles will make a wrong turn in the next hour?
   2. What is the probability that no vehicles will make a wrong turn in the next hour?
   3. If the city's engineering department plans to monitor the intersection for a 4-hour period, what is the probability that more than 20 vehicles will make a wrong turn during this time?
2. In a mechanical engineering workshop, ball bearings are used in various machinery. The lifetime, TT (in hours), of a specific type of ball bearing is known to follow an Exponential distribution with a mean lifetime of 5,000 hours.
   1. What is the probability that one randomly selected ball bearing will last more than 6,000 hours?
   2. What is the probability that one randomly selected ball bearing will last less than 2,500 hours?