79) Which distribution is helpful in testing hypotheses about variances?
A) binomial distribution
B) F distribution
C) normal distribution
D) Poisson distribution
E) exponential distribution
80) A company is considering producing two new electronic games designed for the popular Gameboy toy.
Based on market data, management believes there is a 60 percent chance that a “cops and robbers” game will be
successful and a 40 percent chance that a “let’s play house” game will be successful. As these products are
completely different, it may be assumed that the success of one is totally independent of the success of the other.
If two products are introduced to the market, what is the probability that both are successful?
A) 0.12
B) 0.60
C) 0.36
D) 0.24
E) None of the above
81) A company is considering producing two new electronic games designed for the popular Gameboy toy.
Based on market data, management believes that there is a 60 percent chance that a “cops and robbers” game will
be successful and a 40 percent chance that “let’s play house” game will be successful. As these products are
completely different, it may be assumed that the success of one is totally independent of the success of the other.
If two products are introduced to the market, what is the probability that both are failures?
A) 0.16
B) 0.24
C) 0.80
D) 0.36
E) None of the above
82) A company is considering producing some new Gameboy electronic games. Based on past records,
management believes that there is a 70 percent chance that each of these will be successful and a 30 percent
chance of failure. Market research may be used to revise these probabilities. In the past, the successful products
were predicted to be successful based on market research 90 percent of the time. However, for products that
failed, the market research predicted these would be successes 20 percent of the time. If market research is
performed for a new product, what is the probability that the results indicate a successful market for the product
and the product actually is successful?
A) 0.90
B) 0.54
C) 0.60
D) 0.63
E) None of the above
83) The expected value of a probability distribution is
A) the measure of the spread of the distribution.
B) the variance of the distribution.
C) the average value of the distribution.
D) the probability density function.
E) the range of continuous values from point A to point B, inclusive.
84) Which of the following is not true for discrete random variables?
A) The expected value is the weighted average of the values.
B) They can assume only a countable number of values.
C) The probability of each value of the random variable must be 0.
D) The probability values always sum up to 1.
E) A binomial random variable is considered discrete.
85) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, or 2. The
probabilities are the same for each of these (1/3). If X is the number of calls arriving in a five–minute time period,
what is the mean of X?
A) 1/3
B) 2/3
C) 1
D) 4/3
E) None of the above
86) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, 2, 3, 4, 5, or 6.
The probabilities are the same for each of these (1/7). If X is the number of calls arriving in a five–minute time
period, what is the mean of X?
A) 2
B) 3
C) 4
D) 5
E) None of the above
87) A discrete random variable has a mean of 400 and a variance of 64. What is the standard deviation?
A) 64
B) 8
C) 20
D) 400
E) None of the above
88) Which of the following is not true about continuous random variables?
A) They have an infinite set of values.
B) The area under each of the curves represents probabilities.
C) The entire area under each of the curves equals 1.
D) Some may be described by uniform distributions or exponential distributions.
E) They can only be integer values.
89) Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial
process is assumed, then in a sample of 20 cable customers, what is the probability that exactly 2 customers would
be willing to switch their cable?
A) 0.1
B) 0.04
C) 0.137
D) 0.206
E) 0.794
90) Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial
process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers
would be willing to switch their cable?
A) 0.85
B) 0.15
C) 0.20
D) 0.411
E) 0.589
91) Properties of the normal distribution include
A) a continuous bell–shaped distribution.
B) a discrete probability distribution.
C) the number of trials is known and is either 1, 2, 3, 4, 5, etc.
D) the random variable can assume only a finite or limited set of values.
E) use in queuing.
92) Which of the following characteristics is true for a normal probability distribution?
A) The area under the curve is 1.
B) It is symmetrical.
C) The midpoint is also the mean.
D) Sixty–eight percent of the area under the curve lies within one standard deviation of the mean.
E) All of the above are true.
93) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of
500 and a standard deviation of 50. What is the probability that a student uses fewer than 600 minutes?
A) 0
B) 0.023
C) 0.841
D) 0.977
E) None of the above
94) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of
500 and a standard deviation of 50. What is the probability that a student uses fewer than 400 minutes?
A) 0
B) 0.023
C) 0.159
D) 0.977
E) None of the above
95) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of
500 and a standard deviation of 50. What is the probability that a student uses more than 350 minutes?
A) 0.001
B) 0.999
C) 0.618
D) 0.382
E) None of the above
96) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of
500 and a standard deviation of 50. What is the probability that a student uses more than 580 minutes?
A) 0.152
B) 0.0548
C) 0.848
D) 0.903
E) None of the above
97) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a
home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average
price per square foot for a home is greater than $110?
A) 0
B) 0.023
C) 0.841
D) 0.977
E) None of the above
98) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a
home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average
price per square foot for a home is greater than $90?
A) 0
B) 0.023
C) 0.159
D) 0.977
E) None of the above
99) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a
home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average
price per square foot for a home is less than $85?
A) 0.001
B) 0.999
C) 0.618
D) 0.382
E) None of the above
100) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for
a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average
price per square foot for a home is less than $108?
A) 0.152
B) 0.097
C) 0.848
D) 0.945
E) None of the above
101) The time required to complete a project is normally distributed with a mean of 80 weeks and a standard
deviation of 10 weeks. The construction company must pay a penalty if the project is not finished by the due date
in the contract. If a construction company bidding on this contract puts in a due date of 80 weeks, what is the
probability that they will have to pay a penalty?
A) 0
B) 1.000
C) 0.500
D) 1/8
E) None of the above
102) The time required to complete a project is normally distributed with a mean of 80 weeks and a standard
deviation of 10 weeks. The construction company must pay a penalty if the project is not finished by the due date
in the contract. If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the
due date, what due date (project week #) should be negotiated?
A) 81.28
B) 92.8
C) 81.82
D) .81954
E) None of the above
103) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed
with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take less
than 40 minutes?
A) 0.50
B) 0.20
C) 0.80
D) 1.00
E) None of the above
104) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed
with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take less
than 35 minutes?
A) 0.84134
B) 0.15866
C) 0.53983
D) 0.46017
E) None of the above
105) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed
with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take more
than 40 minutes?
A) 0.2500
B) 0.0625
C) 1.000
D) 0.5000
E) None of the above
106) Queuing Theory makes use of the
A) normal probability distribution.
B) uniform probability distribution.
C) binomial probability distribution.
D) Poisson probability distribution.
E) None of the above
107) The number of cars passing through an intersection in the next five minutes can usually be described by the
A) normal distribution.
B) uniform distribution.
C) exponential distribution.
D) Poisson distribution.
E) None of the above
108) Arrivals at a fast–food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per
hour. What is the probability that in the next hour there will be exactly 12 arrivals?
A) 0.0000
B) 0.0661
C) 0.7500
D) 0.1322
E) None of the above
109) Arrivals at a fast–food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per
hour. What is the probability that in the next hour there will be exactly 8 arrivals?
A) 1.000
B) 0.200
C) 0.175
D) 0.825
E) None of the above
110) Which of the following statements concerning the F distribution is true?
A) The F distribution is discrete.
B) The F distribution is symmetrical.
C) The F distribution is useful in modeling customer arrivals.
D) The F distribution is useful in testing hypotheses about variance.
E) The F distribution is interchangeable with the normal distribution for large sample sizes.
111) What is the F value associated with α = 0.05, numerator degrees of freedom (df1) equal to 4, and denominator
degrees of freedom (df2) equal to 9?
A) 3.63
B) 1.80
C) 6.0
D) 0.11
E) 0.18
112) Which of the following characteristics is not true for the exponential distribution?
A) It is discrete probability distribution.
B) It is also called the negative exponential distribution.
C) It is used in dealing with queuing problems.
D) It is used to describe the times between customer arrivals.
E) The variance is the square of the expected value.
113) The length of time that it takes the tollbooth attendant to service each driver can typically be described by the
A) normal distribution.
B) uniform distribution.
C) exponential distribution.
D) Poisson distribution.
E) None of the above
114) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute)
when it comes to license renewals. The service time follows an exponential distribution. What is the probability
that it will take less than 2 minutes for a particular customer to get a license renewal?
A) 1
B) 0.487
C) 0.513
D) 0
E) 0.1
115) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute)
when it comes to license renewals. The service time follows an exponential distribution. What is the probability
that it will take less than 3 minutes for a particular customer to get a license renewal?
A) 0.5
B) 0
C) 1
D) 0.368
E) 0.632
116) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between
consecutive driver arrivals follows an exponential distribution. What is the probability that takes less than 1/2 of a
minute between consecutive drivers?
A) 0.167
B) 0.223
C) 0.777
D) 0.5
E) 1
117) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between
consecutive driver arrivals follows an exponential distribution. What is the probability that takes more than 1/3 of
a minute between consecutive drivers?
A) 0.632
B) 0.111
C) 0.368
D) 0.632
E) Not enough information given
118) An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the
probability of:
(a) drawing three yellow chips.
(b) drawing a blue chip on the first draw and a yellow chip on the second draw.
(c) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw.
(d) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.
(e) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw.
119) A market research study is being conducted to determine if a product modification will be well received by
the public. A total of 1,000 consumers are questioned regarding this product.
The table below provides information regarding this sample.
Positive
Reaction
Neutral
Reaction
Negative
Reaction
Male
240
60
100
Female
260
220
120
(a) What is the probability that a randomly selected male would find this change unfavorable (negative)?
(b) What is the probability that a randomly selected person would be a female who had a positive reaction?
(c) If it is known that a person had a negative reaction to the study, what is the probability that the person is
male?
120) In a production run of 300 units, there are exactly 20 defective items and 280 good items.
(a) What is the probability that a randomly selected item is defective?
(b) If two items are sampled without replacement, what is the probability that both are good?
(c) If two items are randomly sampled without replacement, what is the probability that the first is good but
the second is defective?
121) A new television program was viewed by 200 people (120 females and 80 males). Of the females, 60 liked the
program and 60 did not. Of the males, 60 of the 80 liked the program.
(a) What is the probability that a randomly selected individual liked the program?
(b) If a male in this group is selected, what is the probability that he liked the program?
(c) What is the probability that a randomly selected individual is a female and liked the program?
122) Colonel Motors (an automobile company) has prepared a marketing campaign for its best selling car. The
focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no complaints
in the first year. You and your sister Kim have each purchased one of these cars.
(a) What is the probability that neither of you has a complaint about the car in the first year if the advertising
claim is true?
(b) What is the probability that exactly one of you has a complaint about the car in the first year if the
advertising claim is true?
123) A local “home TV repair service” company has two repairmen who make all of the home repairs. The
company sends Repairman D on 70 percent of all jobs, because the likelihood of a “second follow–up call” within a
week is only 0.08 compared to 0.20 for Repairman K. If you had a recent repair job that is going to require a
second follow–up call, what is the probability that Repairman K did your initial repair work?
124) Our department store is having a sale on personal computers, of which three are in stock (no rain checks).
There is a certain probability of selling none. The probability of selling one is twice as great as the probability of
selling none. The probability of selling two is three times the probability of selling none. Finally, the probability
of selling all the personal computers is four times as great as the probability of selling none. In a table, list the
outcomes and their probabilities. Hint: Let the probability of selling none equal x.
0.1
0.2
0.3
0.4
125) ABC Manufacturing has 6 machines that perform a particular task. Breakdowns occur frequently for this
machine. Past records indicate that the number of breakdowns that occur each day is described by the following
probability distribution:
Number of
Breakdowns
Probability
0
0.4
1
0.3
2
0.2
3
0.1
More than 3
0.0
(a) What is the expected number of breakdowns in any given day?
(b) What is the variance for this distribution?
(c) What is the probability that there will be at least 2 breakdowns in a day?
126) Fast Service Store has maintained daily sales records on the various size “Cool Drink” sales.
“Cool Drink” Price
Number Sold
$0.50
75
$0.75
120
$1.00
125
$1.25
80
Total
400
Assuming that past performance is a good indicator of future sales,
(a) what is the probability of a customer purchasing a $1.00 “Cool Drink?”
(b) what is the probability of a customer purchasing a $1.25 “Cool Drink?”
(c) what is the probability of a customer purchasing a “Cool Drink” that costs greater than or equal to $1.00?
(d) what is the expected value of a “Cool Drink”?
(e) what is the variance of a “Cool Drink”?
127) In a given office, the color printer breaks down with a probability of 20% in any month. A binomial process
is assumed for a period of 10 months.
(a) What is the probability that the printer breaks down exactly 2 times?
(b) What is the probability that the printer breaks down at most 1 time?
(c) What is the probability that the printer breaks down more than once?
128) A southwestern tourist city has records indicating that the average daily temperature in the summer is 82
degrees F, which is normally distributed with a standard deviation of 3 degrees F. Based on these records,
determine:
(a) the probability of a daily temperature between 79 degrees F and 85 degrees F.
(b) the probability that the daily temperature exceeds 90 degrees F.
(c) the probability that the daily temperature is below 76 degrees F.
129) Using the table for finding the areas under normal curves, find the area under a normal curve with a mean of
200 and a standard deviation of 10 between the values of:
(a) 200 to 205.
(b) 195 to 205.
(c) 200 to 215.
(d) 195 to 215.
(e) 186.5 to 217.
131) Compute the F value based on the following:
(a) df1 = 2, df2 = 4, α = 0.01
(b) df1 = 3 df2 = 6, α = 0.05
132) A call center receives calls from customers at a rate of 2 per min. The time between customer calls follows an
exponential distribution.
(a) What is the probability that it takes 1/3 of a minute or less between consecutive customer calls?
(b) What is the probability that it take 1/2 of a minute or more between consecutive customer calls?
133) Arrivals in a university advising office during the week of registration are known to follow a Poisson
distribution with an average of 4 people arriving each hour.
(a) What is the probability that exactly 4 people will arrive in the next hour?
(b) What is the probability that exactly 5 people will arrive in the next hour?
134) Explain why event probabilities range from 0 to 1.
135) Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively
exhaustive.
136) Name five common probability distributions.
137) If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring?
138) If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring?
139) If two events (A,B) are independent, what is their joint probability?
140) If two events (A,B) are dependent, what is the conditional probability of P(A|B)?
141) If two events (A,B) are independent, then the conditional probability of P(A|B) = ________.
142) Explain what a discrete random variable is.
143) The exponential distribution often describes ________.
144) List the two parameters of the normal distribution.
145) In what way is the F distribution often used?
146) List the parameter(s) of the Poisson distribution.