202Part 2: Probability6.64 A town council includes 10 Democrats and 156.72 According to the U.S. Centers for Disease ControlRepublicans. In response to a developer's request for avariance that would allow her to build a convenienceand Prevention, Americans 85 years of age and olderexperience flu-associated respiratory and circulatoryillness at an annual rate of approximately 1200 casesstore in an area of town currently zoned as residential.the mayor is going to randomly select 5 council mem-bersper 100,000 persons. If a rural county has 500 seniprobability that noof them will experience such an illness duringcoming year? If, in such a county, 15 seniors in thisage group were to come down with such an illnessduring the coming year, would this be considered ratherunusual? Explain your conclusion. Source: Anita Manning,seniorsin this age group, what isthanfora committee to examine the issue. What is theno moreprobability that there will be at least 3 Republicans onthe committee?56.65 Fred and Emily are among the 50 finalists in a lot-tery in which 5 winners will be randomly selected toreceive a free vacation in Hawaii. Using the hypergeo-metric distribution, determine the probability that exactly Expected." USA Today, September 15, 2004, p. 5D."Tens of Thousands More People Are Hospitalized for Flu Thanone of these two individuals will win a free vacation.6.66 Seven of the 15 campus police officers available forassignment to the auditorium in which a local politicianis to speak have received advanced training in crowdcontrol. If 5 officers are randomly selected for serviceduring the speech, what is the probability that exactly2 of them will have had advanced training in crowdcontrol? What is the probability that at least 3 of themwill have had advanced training?6.73 Although they have no commercials, publictelevision stations periodically conduct campaigns dur-ing which programming is occasionally interrupted byappeals for subscriber donations. A local publictelevision station has found that, during these breaks,the number of calls averages 3 per minute. It hasrecently upgraded the switchboard so it can handle asmany as 5 calls per minute. The station is now in themiddle of a program break. What is the probabilitythat the switchboard will be overloaded during the nextminute?6.67 A producer of copper tubing has found that, on theaverage, five flaws occur per 2000 feet of tubing. Thetubing is sold in continuous rolls of 200 feet each. Whatis the probability that a randomly selected 200-foot rollwill have no flaws?6.74 A gorilla once made headlines in 400 newspapersand appeared on three national television shows aftercorrectly "selecting" the winner of 13 out of 20 footballgames. He had made his "choice" for each game bygrabbing one of two pieces of paper on which the namesof the teams were written. If a great many gorillas hadthe same opportunity, what percentage of them wouldbe at least this lucky? Source: "Gone Ape," Pittsburgh Press,6.68 A large plumbing contractor buys eight 200-footrolls from the producer described in Exercise 6.67.Determine the probability that no more than three of theeight rolls will be flawless.6.69 In 2004, 50% of all U.S. families had a net worthless than $93,000. What is the probability that exactlythree of a randomly selected sample of five families wouldhave a net worth less than $93,000? Source: StatisticalJune 8, 1986.6.75 It has been estimated that over 90% of the world'slarge corporations are actively involved in data ware-housing. Using the 90% figure, and considering a ran-dom sample of 10 large corporations, what is the prob-ability that at least 7 of them are actively involved indata warehousing?Abstract of the United States 2009, p. 459.6.70 A trucking company has found that its trucks aver-age 0.2 breakdowns during round trips from New Yorkto Los Angeles.a. What is the probability that a single truck will makethe complete trip without experiencing a breakdown? plete rounds played by a member during a given outingb. If 3 trucks are assigned to a NY/LA round trip, whatis the probability that at least 2 of them will makethe complete trip without experiencing a breakdown? on his or her next outing?6.76 A country club has found that the number of com-averages 1.3 rounds. What is the probability that a golferselected at random will complete at least 2 rounds of golf6.71 The Bureau of Labor Statistics says that baggagehandlers, trash haulers, and coal miners are among theoccupations having the highest risk of a debilitatinginjury or illness. For coal miners workingof a year, the injury rate has been reported as 3.6 injuriesper 100 coal miners. For a company that employs 200coal miners, what is the probability that at least 10 ofits workers will experience a debilitating injury or ill-ness over the next year? Source: "Workers at Risk," USA Today,6.77 A computer manufacturer that sells notebookcomputers directly to customers has been havingproblems with one of its models-it seems that about10% of the units are inoperable upon arrival to thecustomer. They are functional when tested at the factory,but there is some problem associated with the shipping/handling process that the company's engineers have notyet been able to identify and correct. A highly valuedcustomer places an emergency order for 8 of thesenotebooks, and wants them delivered overnight andtheurseMarch 15, 2006, р. 6D.

We are allowed to answer one question at a time. We’ll answer the first question since the exact one…

6.64 A town council includes 10 Democrats and 15 Republicans. In response to a developer's request for a variance that would allow her to build a convenience store in an area of town currently zoned as residential, the mayor is going to randomly select 5 council mem- bers for a committee to examine the issue. What is the probability that there will be at least 3 Republicans on the committee?

6.64 A town council includes 10 Democrats and 15 Republicans. In response to a developer's request for a variance that would allow her to build a convenience store in an area of town currently zoned as residential, the mayor is going to randomly select 5 council mem- bers for a committee to examine the issue. What is the probability that there will be at least 3 Republicans on the committee?

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

202
Part 2: Probability
6.64 A town council includes 10 Democrats and 15
6.72 According to the U.S. Centers for Disease Control
Republicans. In response to a developer's request for a
variance that would allow her to build a convenience
and Prevention, Americans 85 years of age and older
experience flu-associated respiratory and circulatory
illness at an annual rate of approximately 1200 cases
store in an area of town currently zoned as residential.
the mayor is going to randomly select 5 council mem-
bers
per 100,000 persons. If a rural county has 500 seni
probability that no
of them will experience such an illness during
coming year? If, in such a county, 15 seniors in this
age group were to come down with such an illness
during the coming year, would this be considered rather
unusual? Explain your conclusion. Source: Anita Manning,
seniors
in this age group, what is
than
for
a committee to examine the issue. What is the
no more
probability that there will be at least 3 Republicans on
the committee?
5
6.65 Fred and Emily are among the 50 finalists in a lot-
tery in which 5 winners will be randomly selected to
receive a free vacation in Hawaii. Using the hypergeo-
metric distribution, determine the probability that exactly Expected." USA Today, September 15, 2004, p. 5D.
"Tens of Thousands More People Are Hospitalized for Flu Than
one of these two individuals will win a free vacation.
6.66 Seven of the 15 campus police officers available for
assignment to the auditorium in which a local politician
is to speak have received advanced training in crowd
control. If 5 officers are randomly selected for service
during the speech, what is the probability that exactly
2 of them will have had advanced training in crowd
control? What is the probability that at least 3 of them
will have had advanced training?
6.73 Although they have no commercials, public
television stations periodically conduct campaigns dur-
ing which programming is occasionally interrupted by
appeals for subscriber donations. A local public
television station has found that, during these breaks,
the number of calls averages 3 per minute. It has
recently upgraded the switchboard so it can handle as
many as 5 calls per minute. The station is now in the
middle of a program break. What is the probability
that the switchboard will be overloaded during the next
minute?
6.67 A producer of copper tubing has found that, on the
average, five flaws occur per 2000 feet of tubing. The
tubing is sold in continuous rolls of 200 feet each. What
is the probability that a randomly selected 200-foot roll
will have no flaws?
6.74 A gorilla once made headlines in 400 newspapers
and appeared on three national television shows after
correctly "selecting" the winner of 13 out of 20 football
games. He had made his "choice" for each game by
grabbing one of two pieces of paper on which the names
of the teams were written. If a great many gorillas had
the same opportunity, what percentage of them would
be at least this lucky? Source: "Gone Ape," Pittsburgh Press,
6.68 A large plumbing contractor buys eight 200-foot
rolls from the producer described in Exercise 6.67.
Determine the probability that no more than three of the
eight rolls will be flawless.
6.69 In 2004, 50% of all U.S. families had a net worth
less than $93,000. What is the probability that exactly
three of a randomly selected sample of five families would
have a net worth less than $93,000? Source: Statistical
June 8, 1986.
6.75 It has been estimated that over 90% of the world's
large corporations are actively involved in data ware-
housing. Using the 90% figure, and considering a ran-
dom sample of 10 large corporations, what is the prob-
ability that at least 7 of them are actively involved in
data warehousing?
Abstract of the United States 2009, p. 459.
6.70 A trucking company has found that its trucks aver-
age 0.2 breakdowns during round trips from New York
to Los Angeles.
a. What is the probability that a single truck will make
the complete trip without experiencing a breakdown? plete rounds played by a member during a given outing
b. If 3 trucks are assigned to a NY/LA round trip, what
is the probability that at least 2 of them will make
the complete trip without experiencing a breakdown? on his or her next outing?
6.76 A country club has found that the number of com-
averages 1.3 rounds. What is the probability that a golfer
selected at random will complete at least 2 rounds of golf
6.71 The Bureau of Labor Statistics says that baggage
handlers, trash haulers, and coal miners are among the
occupations having the highest risk of a debilitating
injury or illness. For coal miners working
of a year, the injury rate has been reported as 3.6 injuries
per 100 coal miners. For a company that employs 200
coal miners, what is the probability that at least 10 of
its workers will experience a debilitating injury or ill-
ness over the next year? Source: "Workers at Risk," USA Today,
6.77 A computer manufacturer that sells notebook
computers directly to customers has been having
problems with one of its models-it seems that about
10% of the units are inoperable upon arrival to the
customer. They are functional when tested at the factory,
but there is some problem associated with the shipping/
handling process that the company's engineers have not
yet been able to identify and correct. A highly valued
customer places an emergency order for 8 of these
notebooks, and wants them delivered overnight and
the
urse
March 15, 2006, р. 6D.

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