Nama : Devi Wijaya Putri

NIM : 3333170023
Kelas : A (Teori Probabilitas)
EXCERSISE 3-9
3.157. Suppose that X has a Poisson distribution with a
mean of 4. Determine the following probabilities:
a. P(X = 0)
b. P(X ≤ 2)
c. P(X = 4)
d. P(X = 8)

3.158. Suppose that X has a Poisson distribution with a

mean of 0.4. Determine the following probabilities:
a. P(X = 0)
b. P(X ≤ 2)
c. P(X = 4)
d. P(X = 8)

3.159. Suppose that the number of customers who enter a

bank in an hour is a Poisson random variable, and
suppose that P(X = 0) = 0.05. Determine the mean
and variance of X.

3.160. The number of telephone calls that arrive at a

phone exchange is often modeled as a Poisson
random variable. Assume that on the average there
are 10 calls per hour.
a. What is the probability that there are exactly 5
calls in one hour?
b. What is the probability that there are 3 or fewer
calls in one hour?
c. What is the probability that there are exactly 15
calls in two hours?
d. What is the probability that there are exactly 5
calls in 30 minutes?

3.161. Astronomers treat the number of stars in a given

volume of space as a Poisson random variable. The
density in the Milky Way Galaxy in the vicinity of
our solar system is one star per 16 cubic light-years.
a. What is the probability of two or more stars in
16 cubic light-years?
b. How many cubic light-years of space must be
studied so that the probability of one or more
stars exceeds 0.95?

3.162. Data from www.centralhudsonlabs.com

determined the mean number of insect fragments in
225-gram chocolate bars was 14.4, but three brands
 had insect contamination more than twice the
average. See the U.S. Food and Drug
Administration–Center for Food Safety and Applied
Nutrition for Defect Action Levels for food
products. Assume that the number of fragments
(contaminants) follows a Poisson distribution.
a. If you consume a 225-gram bar from a brand at
the mean contamination level, what is the
probability of no insect contaminants?
b. Suppose that you consume a bar that is one-fifth
the size tested (45 grams) from a brand at the
mean contamination level. What is the
probability of no insect contaminants?
c. If you consume seven 28.35-gram (one-ounce)
bars this week from a brand at the mean
contamination level, what is the probability that
you consume one or more insect fragments in
more than one bar?
d. Is the probability of contamination more than
twice the mean of 14.4 unusual, or can it be
considered typical variation? Explain.

3.163. In 1898, L. J. Bortkiewicz published a book

entitled The Law of Small Numbers. He used data
collected over 20 years to show that the number of
soldiers killed by horse kicks each year in each
corps in the Prussian cavalry followed a Poisson
distribution with a mean of 0.61.
a. What is the probability of more than one death
in a corps in a year?
b. What is the probability of no deaths in a corps
over five years?

3.164. The number of flaws in bolts of cloth in textile

manufacturing is assumed to be Poisson distributed
with a mean of 0.1 flaw per square meter.
a. What is the probability that there are two flaws
in one square meter of cloth?
b. What is the probability that there is one flaw in
10 square meters of cloth?
c. What is the probability that there are no flaws in
20 square meters of cloth?
d. What is the probability that there are at least two
flaws in 10 square meters of cloth?

3.165. When a computer disk manufacturer tests a disk, it

writes to the disk and then tests it using a certifier.
The certifier counts the number of missing pulses or
errors. The number of errors on a test area on a disk
has a Poisson distribution with λ = 0 2. .
a. What is the expected number of errors per test
area?
b. What percentage of test areas have two or fewer
errors?
3.166. The number of cracks in a section of interstate
highway that are significant enough to require
repair is assumed to follow a Poisson distribution
with a mean of two cracks per mile.
a. What is the probability that there are no cracks
that require repair in 5 miles of highway?
b. What is the probability that at least one crack
requires repair in 1 2/ mile of highway?
c. If the number of cracks is related to the vehicle
load on the highway and some sections of the
highway have a heavy load of vehicles whereas
other sections carry a light load, what do you
think about the assumption of a Poisson
distribution for the number of cracks that require
repair?

3.167. The number of surface flaws in plastic panels used

in the interior of automobiles has a Poisson
distribution with a mean of 0.05 flaw per square
foot of plastic panel. Assume that an automobile
interior contains 10 square feet of plastic panel.
a. What is the probability that there are no surface
flaws in an auto’s interior?
b. If 10 cars are sold to a rental company, what is
the probability that none of the 10 cars has any
surface flaws?
c. If 10 cars are sold to a rental company, what is
the probability that at most 1 car has any surface
flaws?

3.168. The number of failures of a testing instrument

from contamination particles on the product is a
Poisson random variable with a mean of 0.02
failures per hour.
a. What is the probability that the instrument does
not fail in an 8-hour shift?
b. What is the probability of at least one failure in a
24-hour day?

3.169. The number of content changes to a Web site

follows a Poisson distribution with a mean of 0.25
per day.
a. What is the probability of two or more changes
in a day?
b. What is the probability of no content changes in
five days?
c. What is the probability of two or fewer changes
in five days?

3.170. The number of views of a page on a Web site

follows a Poisson distribution with a mean of 1.5
per minute.
a. What is the probability of no views in a minute?
b. What is the probability of two or fewer views in
10 minutes?
c. Does the answer to the previous part depend on
 whether the 10-minute period is an uninterrupted
interval? Explain.

3.171. Cabs pass your workplace according to a Poisson

process with a mean of five cabs per hour. Suppose
that you exit the workplace at 6:00 p.m. Determine
the following:
a. Probability that you wait more than 10 minutes
for a cab.
b. Probability that you wait fewer than 20 minutes
for a cab.
c. Mean number of cabs per hour so that the
probability that you wait more than 10 minutes
is 0.1.

3.172. Orders arrive at a Web site according to a Poisson

process with a mean of 12 per hour. Determine the
following:
a. Probability of no orders in five minutes.
b. Probability of 3 or more orders in five minutes.
c. Length of a time interval such that the
probability of no orders in an interval of this
length is 0.001.

3.173. The article “An Association Between Fine

Particles and Asthma Emergency Department Visits
for Children in Seattle” [Environmental Health
Perspectives June, 1999 107(6)] used Poisson
models for the number of asthma emergency
department (ED) visits per day. For the zip codes
studied, the mean ED visits were 1.8 per day.
Determine the following:
a. Probability of more than five visits in a day.
b. Probability of fewer than five visits in a week.
c. Number of days such that the probability of at
least one visit is 0.99.
d. Instead of a mean of 1.8 per day, determine the
mean visits per day such that the probability of
more than five visits in a day is 0.1.

3.174. Inclusions are defects in poured metal caused by

contaminants. The number of (large) inclusions in
cast iron follows a Poisson distribution with a mean
of 2.5 per cubic millimeter. Determine the
following:
a. Probability of at least one inclusion in a cubic
millimeter.
b. Probability of at least five inclusions in 5.0
cubic millimeters.
c. Volume of material to inspect such that the
probability of at least one inclusion is 0.99.
d. Instead of a mean of 2.5 per cubic millimeters,
the mean inclusions per cubic millimeter such
that the probability of at least one inclusion is
0.95.