Abs
Content
6.63
As a birthday gift, you are mailing a new personal digital assistant (PDA) to
your cousin in Toledo. The PDA cost $250. There is a 2 percent chance it will be lost
or damaged in the mail. Is it worth $4 to insure mailing? Explain, using the concept of
expected value.
6.66
There is a 14 percent chance that a Noodles & Company customer will order
bread with the meal. Use Excel to find the probability that in a sample of 10
customers (a) more than five will order bread; (b) no more than two will; (c) none of
the 10 will order bread. (d) Is the distribution skewed left or right?
6.67
In a certain year, on average 10 percent of the vehicles tested for emissions
failed the test. Suppose that five vehicles are tested. (a) What is the probability that all
pass? (b) All but one pass? (c) Sketch the probability distribution and discuss its
shape.
6.68
The probability that an American CEO can transact business in a foreign
language is .20. Ten American CEOs are chosen at random. (a) What is the probability
that none can transact business in a foreign language? (b) That at least two can? (c)
That all 10 can?
6.69
In a certain Kentucky Fried Chicken franchise, half of the customers typically
request “crispy” instead of “original”. (a) What is the probability that none of the next
four customers will request “crispy”? (b) At least two? (c) At most two? (d) Construct
the probability distribution (Excel or Appendix A), make a graph of its PDF, and
describe is shape.
6.70
On average, 40 percent of U.S. beer drinkers order light beer. (a) What is the
probability that none of the next eight customers who order beer will order light beer?
(b) That one customer will? (c) Two customers? (d) Fewer than three? (e) Construct
the probability distribution (Excel or Appendix A), make a graph of its PDF, and
describe is shape.
6.71 Write out the Excel binomial formula for each probability.
a)
b)
c)
d)
Three successes in 20 trials with a 30 percent chance of success.
Seven successes in 50 trials with a 10 percent chance of success.
Six or fewer successes in 80 trials with a 5 percent chance of success.
At least 30 successes in 120 trials with a 20 percent chance of success.
6.72
Tired of careless spelling and grammar, a company decides to administer a test
to all job applicants. The test consists of 20 sentences. Applicants must state whether
each sentence contains any grammar or spelling errors. Half the sentences contain
errors. The company requires a score of 14 or more. (a) If an applicant guesses
randomly, what is the probability of passing? (b) What minimum score would be
required to reduce the probability "passing by guessing" to 5 percent or less?
6.73
The default rate on governmentâguaranteed student loans at a certain private 4
year institution is 7 percent. The college extends 10 such loans. (a) What is the
probability that none of them will default? (b) That at least three will default? c) What
is the expected number of defaults?
6.74
Experience indicates that 8 percent of the pairs of men's trousers dropped off
for dry cleaning will have an object in the pocket that should be removed before
cleaning. Suppose that 14 pair of pants are dropped off and the cleaner forgets to
check the pockets. What is the probability that no pair has an object in the pocket?
6.75
A study by the Parents' Television Council showed that 80 percent of movie
commercials aired on network television between 8 and 9 p.m. (the prime family
viewing hour) were for R-rated films. (a) Find the probability that in 16 commercials
during this time slot at least 10 will be for R-rated films. (b) Find the probability of
fewer than 8 R-rated films.
6.76
Write the Excel formula for each Poisson probability, using a mean arrival rate
of 10 arrivals per hour.
(a) Seven arrivals.
(b) Three arrivals.
(c) Fewer than five arrivals.
(d) At least 11 arrivals.
6.77
A small feeder airline knows that the probability is .10 that a reservation holder
will not show up for its daily 7:15 A.M. flight into a hub airport. The flight carries 10
passengers. (a) If the flight is fully booked, what is the probability that all those with
reservations will show up? (b) If the airline overbooks by selling 11 seats, what is the
probability that no one will have to be bumped? (c) That more than one passenger
will be bumped? *(d) The airline wants to overbook the flight by enough seats to
ensure a 95 percent chance that the flight will be full, even if some passengers may
be bumped. How many seats would it sell?
6.78
Although television HDTV converters are tested before they are placed in the
installer's truck, the installer knows that 20 percent of them still won't work properly.
The driver must install eight converters today in an apartment building. (a) Ten
converters are placed in the truck. What is the probability that the driver will have
enough working converters? *(b) How many boxes should the driver load to ensure a
95 percent probability of having enough working converters?
6.86
Car security alarms go off at a mean rate of 3.8 per hour in a large Costco
parking lot. Find the probability that in an hour there will be (a) no alarms; (b) fewer
than four alarms; and (c) more than five alarms.
6.87
In a certain automobile manufacturing paint shop, paint defects on the hood
occur at a mean rate of 0.8 defect per square meter. A hood on a certain car has an
area of 3 square meters. (a) Justify the use of the Poisson model. (b) If a customer
inspects a hood at random, what is the probability that there will be no defects? (c)
One defect? (d) Fewer than two defects?
6.88 Past insurance company audits have found that 2 percent of dependents claimed on
an employee’s health insurance actually are ineligible for health benefits. An auditor
examines a random sample of 7 claimed dependents. (a) What is the probability that
all are eligible? (b) That at least one is ineligible?
7.58
The time it takes a ski patroller to respond to an accident call has an
exponential distribution with an average equal to 5 minutes. (a) In what time will 90
percent of all ski accident calls be responded to? (b) If the ski patrol would like to be
able to respond to 90 percent of the accident calls within 10 minutes, what does the
average response time need to be?
7.59
Between 11 p.m. and midnight on Thursday night, Mystery Pizza
average of 4.2 telephone orders per hour. (a) Find the median waiting time
next telephone order. (b) Find the upper quartile of waiting time before
telephone order. (c) What is the upper 10 percent of waiting time until
telephone order? Show all calculations clearly.
gets an
until the
the next
the next
7.60
A passenger metal detector at Chicago's Midway Airport gives an alarm 0.5
time a minute. (a) Find the median waiting time until the next alarm. (b) Find the first
quartile of waiting time before the next alarm. (c) Find the 30th percentile waiting time
until the next alarm. Show all calculations clearly
As a birthday gift, you are mailing a new personal digital assistant (PDA) to
your cousin in Toledo. The PDA cost $250. There is a 2 percent chance it will be lost
or damaged in the mail. Is it worth $4 to insure mailing? Explain, using the concept of
expected value.
6.66
There is a 14 percent chance that a Noodles & Company customer will order
bread with the meal. Use Excel to find the probability that in a sample of 10
customers (a) more than five will order bread; (b) no more than two will; (c) none of
the 10 will order bread. (d) Is the distribution skewed left or right?
6.67
In a certain year, on average 10 percent of the vehicles tested for emissions
failed the test. Suppose that five vehicles are tested. (a) What is the probability that all
pass? (b) All but one pass? (c) Sketch the probability distribution and discuss its
shape.
6.68
The probability that an American CEO can transact business in a foreign
language is .20. Ten American CEOs are chosen at random. (a) What is the probability
that none can transact business in a foreign language? (b) That at least two can? (c)
That all 10 can?
6.69
In a certain Kentucky Fried Chicken franchise, half of the customers typically
request “crispy” instead of “original”. (a) What is the probability that none of the next
four customers will request “crispy”? (b) At least two? (c) At most two? (d) Construct
the probability distribution (Excel or Appendix A), make a graph of its PDF, and
describe is shape.
6.70
On average, 40 percent of U.S. beer drinkers order light beer. (a) What is the
probability that none of the next eight customers who order beer will order light beer?
(b) That one customer will? (c) Two customers? (d) Fewer than three? (e) Construct
the probability distribution (Excel or Appendix A), make a graph of its PDF, and
describe is shape.
6.71 Write out the Excel binomial formula for each probability.
a)
b)
c)
d)
Three successes in 20 trials with a 30 percent chance of success.
Seven successes in 50 trials with a 10 percent chance of success.
Six or fewer successes in 80 trials with a 5 percent chance of success.
At least 30 successes in 120 trials with a 20 percent chance of success.
6.72
Tired of careless spelling and grammar, a company decides to administer a test
to all job applicants. The test consists of 20 sentences. Applicants must state whether
each sentence contains any grammar or spelling errors. Half the sentences contain
errors. The company requires a score of 14 or more. (a) If an applicant guesses
randomly, what is the probability of passing? (b) What minimum score would be
required to reduce the probability "passing by guessing" to 5 percent or less?
6.73
The default rate on governmentâguaranteed student loans at a certain private 4
year institution is 7 percent. The college extends 10 such loans. (a) What is the
probability that none of them will default? (b) That at least three will default? c) What
is the expected number of defaults?
6.74
Experience indicates that 8 percent of the pairs of men's trousers dropped off
for dry cleaning will have an object in the pocket that should be removed before
cleaning. Suppose that 14 pair of pants are dropped off and the cleaner forgets to
check the pockets. What is the probability that no pair has an object in the pocket?
6.75
A study by the Parents' Television Council showed that 80 percent of movie
commercials aired on network television between 8 and 9 p.m. (the prime family
viewing hour) were for R-rated films. (a) Find the probability that in 16 commercials
during this time slot at least 10 will be for R-rated films. (b) Find the probability of
fewer than 8 R-rated films.
6.76
Write the Excel formula for each Poisson probability, using a mean arrival rate
of 10 arrivals per hour.
(a) Seven arrivals.
(b) Three arrivals.
(c) Fewer than five arrivals.
(d) At least 11 arrivals.
6.77
A small feeder airline knows that the probability is .10 that a reservation holder
will not show up for its daily 7:15 A.M. flight into a hub airport. The flight carries 10
passengers. (a) If the flight is fully booked, what is the probability that all those with
reservations will show up? (b) If the airline overbooks by selling 11 seats, what is the
probability that no one will have to be bumped? (c) That more than one passenger
will be bumped? *(d) The airline wants to overbook the flight by enough seats to
ensure a 95 percent chance that the flight will be full, even if some passengers may
be bumped. How many seats would it sell?
6.78
Although television HDTV converters are tested before they are placed in the
installer's truck, the installer knows that 20 percent of them still won't work properly.
The driver must install eight converters today in an apartment building. (a) Ten
converters are placed in the truck. What is the probability that the driver will have
enough working converters? *(b) How many boxes should the driver load to ensure a
95 percent probability of having enough working converters?
6.86
Car security alarms go off at a mean rate of 3.8 per hour in a large Costco
parking lot. Find the probability that in an hour there will be (a) no alarms; (b) fewer
than four alarms; and (c) more than five alarms.
6.87
In a certain automobile manufacturing paint shop, paint defects on the hood
occur at a mean rate of 0.8 defect per square meter. A hood on a certain car has an
area of 3 square meters. (a) Justify the use of the Poisson model. (b) If a customer
inspects a hood at random, what is the probability that there will be no defects? (c)
One defect? (d) Fewer than two defects?
6.88 Past insurance company audits have found that 2 percent of dependents claimed on
an employee’s health insurance actually are ineligible for health benefits. An auditor
examines a random sample of 7 claimed dependents. (a) What is the probability that
all are eligible? (b) That at least one is ineligible?
7.58
The time it takes a ski patroller to respond to an accident call has an
exponential distribution with an average equal to 5 minutes. (a) In what time will 90
percent of all ski accident calls be responded to? (b) If the ski patrol would like to be
able to respond to 90 percent of the accident calls within 10 minutes, what does the
average response time need to be?
7.59
Between 11 p.m. and midnight on Thursday night, Mystery Pizza
average of 4.2 telephone orders per hour. (a) Find the median waiting time
next telephone order. (b) Find the upper quartile of waiting time before
telephone order. (c) What is the upper 10 percent of waiting time until
telephone order? Show all calculations clearly.
gets an
until the
the next
the next
7.60
A passenger metal detector at Chicago's Midway Airport gives an alarm 0.5
time a minute. (a) Find the median waiting time until the next alarm. (b) Find the first
quartile of waiting time before the next alarm. (c) Find the 30th percentile waiting time
until the next alarm. Show all calculations clearly
