2.14 The Poisson Process
167 2. Deaths in a small city occur at a rate of 5 per week and are known to follow a
Poisson distribution.
a. What is the expected number of deaths in a three-day period? b. What is the probability no one dies in a three-day period?
c. What is the probability that at least 250 people die in 52 weeks? 3. Traffic accidents at an intersection are assumed to follow a Poisson distribution
with 4 accidents expected in a period of one year.
a. What is the probability of, at most, one accident in a given year? b. What is the probability of exactly 3 accidents in 6 months?
c. It is expected that 2 accidents occur during a year at another intersection. What
is the probability that there is a total of at least 3 accidents in a given year at the 2 intersections?
4. The number of typographical errors per page in a book follows a Poisson distribu-
tion with parameter
3 4
. What is the probability that there is a total of 10 errors on 10 randomly selected pages in the book?
5. Twenty percent of the IC chips made in a plant are nonfunctional. Assume that a
binomial model is appropriate.
a. Find the probability that at most 13 nonfunctional chips occur in a sample of
100 chips.
b. Use the Poisson distribution to approximate the result in part a. 6. Let X, the number of hits in a baseball game, be a Poisson variable with parameter
Þ: If the probability of a no-hit game is
1 3
, what is Þ?
7. An insurance company has discovered that about 0.1 of the population is involved
in a certain type of accident each year. If the 10,000 policy holders of the company are randomly selected from the population, what is the probability that not more
than 5 of its clients are involved in such an accident next year?
8. A study of customers entering a grocery store shows that all the arrivals are Poisson
with males entering at an average rate of 3 per minute and females at an average rate of 5 per minute. Find the probability that at least 20 customers enter the store
in the next 5 minutes.
9. Computer programs run on a certain computer are executed during an interval of
one minute according to a Poisson process with mean 12. Twenty-five percent of these programs utilize a plotter.
a. What is the probability there will be a demand for at least 15 programs run in