Deck 5: Discrete Probability Distributions

Question 1

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 7 times, keeping track of the winning numbers.

A) Not binomial: there are more than two outcomes for each trial.
B) Not binomial: there are too many trials.
C) Not binomial: the trials are not independent.
D) The procedure results in a binomial distribution.

Answer 1

A

Question 2

Answer 2

D

Question 3

A) Yes
B) No

Answer 3

B

Question 4

Question 5

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled.

Question 6

Question 7

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

A) 7.5 twos
B) 3 twos
C) 2.25 twos
D) 1.5 twos

Question 8

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

A) 7.5 twos
B) 3 twos
C) 2.25 twos
D) 1.5 twos

Question 9

Question 10

Use the given values of to find the minimum value that is not significantly low, , and the maximum value that is not significantly high, Round your answer to the nearest hundredth unless
Otherwise noted.

A) Minimum: 1478.7; maximum: 1689.3
B) Minimum: 1544.2; maximum: 1623.8
C) Minimum: 1623.8; maximum: 1544.2
D) Minimum: 1564.1; maximum: 1603.9

Question 11

In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.

A) 66 adults
B) 344 adults
C) 34 adults
D) 669 adults

Question 12

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will
Have a flat tire. Round your answer to four decimal places.

A) 0.1217
B) 0.1947
C) 0.1460
D) 0.8783
E) 0.1703

Question 13

On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

A) 4.3 questions
B) 12.8 questions
C) 5.7 questions
D) 8.5 questions

Question 14

Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are
Considered morbidly obese. Is it significant to have no obese subjects among three randomly selected
Adolescents?

A) Yes
B) No

Question 15

Question 16

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least
Two wrong numbers. Round your answer to four decimal places.

A) 0.1991
B) 0.8009
C) 0.7760
D) 0.2240
E) 0.5768

Question 17

In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.

Question 18

The braking time of a car. Identify the given random variable as being discrete or continuous.

A) Discrete
B) Continuous

Question 19

Question 20

Question 21

A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to approximate the probability that
The number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate
Poisson distribution (the mean number of cases in groups of 74,090 children).

A) 2.7
B) 0.000037
C) 27,400
D) 274

Question 22

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars
That failed among six that were tested for roadworthiness: Find the probability of getting three or more cars that fail among six cars tested.

A) 0.222
B) 0.048
C) 0.005
D) 0.046

Question 23

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others.

A) 0.0635
B) 0.00184
C) 0.154
D) 0.133

Question 24

Determine whether the following is a probability distribution. If not, identify the requirement that is not
satisfied.

Question 25

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

A) Continuous
B) Discrete

Question 26

Determine whether the following is a probability distribution. If not, identify the requirement that is not
satisfied.

Question 27

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 53 times, keeping track of the "fives" rolled.

A) The procedure results in a binomial distribution.
B) Not binomial: the trials are not independent.
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: there are too many trials.

Question 28

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x represents the number of cars
That failed among six that were tested for roadworthiness: Is the probability of getting three or more cars that fail among six cars tested significant, determined by a cutoff value of
0)05?

A) Yes
B) No

Question 29

A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800,
Would it be significant to get 634 consumers who recognize the Dull Computer Company name? Consider as
Significant any result that differs from the mean by more than 2 standard deviations. That is, significant values
Are either less than or greater than

A) Yes
B) No

Question 30

Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected. Find the probability that
Fewer than three of the selected adults watch prime-time live.

A) 0.000358
B) 0.00430
C) 0.0512
D) 0.00467

Question 31

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "16."

A) Not binomial: there are more than two outcomes for each trial.
B) The procedure results in a binomial distribution..
C) Not binomial: the trials are not independent.
D) Not binomial: there are too many trials.

Question 32

Find the standard deviation, σ, for the binomial distribution with n = 38 and p = 0.4.

Question 33

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

A) 5.8 defects
B) 1.8 defects
C) 18 defects
D) 0.2 defects

Question 34

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

A) 2.8 students
B) 0.2 students
C) 4.0 students
D) 3.5 students

Question 35

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three
Decimal places.

A) 0.172
B) 0.377
C) 0.205
D) 0.828

Question 36

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 26 times, keeping track of the numbers that are rolled.

A) Not binomial: there are more than two outcomes for each trial.
B) Not binomial: the trials are not independent.
C) Not binomial: there are too many trials.
D) The procedure results in a binomial distribution.

Question 37

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority? Round to
Three decimal places.

A) 0.985
B) 0.982
C) 0.913
D) 0.055

Question 38

A) Yes
B) No

Question 39

In one town, the number of burglaries in a week has a Poisson distribution with a mean of 1.9 burglaries. Find the probability that in a randomly selected week the number of burglaries is at least three. Use the Poisson
Distribution to find the indicated probability.

A) 0.8290
B) 0.1710
C) 0.1253
D) 0.2963
E) 0.7037

Question 40

Use the given values of n = 1205 and p = 0.98 to find the minimum value that is not significantly low, and the maximum value that is not significantly high, Round your answer to the nearest hundredth unless
Otherwise noted.

A) Minimum: 1190.62 ; maximum: 1171.18
B) Minimum: 1171.18; maximum: 1190.62
C) Minimum: 1176.04; maximum: 1185.76
D) Minimum: 1174.03; maximum: 1187.77

Question 41

In a magazine survey, 427 women are randomly selected without replacement and each woman is asked what
she purchases online. Responses consist of whether clothing was identified. Determine whether the given
procedure results in a distribution that is either binomial or can be treated as binomial. If not binomial, identify
at least one requirement that is not satisfied.

Question 42

An experiment consists of rolling a single die 12 times and the variable x is the number of times that the
outcome is 6. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3
times, why or why not?

Question 43

Multiple-choice questions on a test each have 5 possible answers, one of which is correct.
Assume that you guess the answers to 5 such questions.
a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the last 3 guesses are correct.
That is, find P(WWCCC), where C denotes a correct answer and W denotes a wrong answer.
b. Make a complete list of the different possible arrangements of 2 wrong answers and 3 correct answers, then find the
probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly 3 correct answers when 5 guesses are made?

Question 44

In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The
table is based on their responses. Determine whether a probability distribution is given and two reasons why or why
not.

Question 45

The cost of a randomly selected orange

A) Continuous
B) Discrete

Question 46

Do probability distributions measure what did happen or what will probably happen?
How do we use probability distributions to make decisions?

Question 47

For the table shown below, the random variable x is the number of males with tinnitus (ringing ears) among
four randomly selected males, based on a medical journal. Find the mean and standard deviation for the
random variable x. Use the range rule of thumb to identify the range of values that are not significant for the
number of males with tinnitus among four randomly selected males. Is getting three males with tinnitus among
four randomly selected males a significantly high number?

Question 48

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said
that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die
to turn up with a value of 3.5, the expected value couldn't possibly be 3.5. Who is right?

Question 49

Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good
investment. Find the probability that among 16 randomly selected people, at least 1 believes that college is no
longer a good investment.

Question 50

Sampling without replacement involves dependent events, so this would not be considered a binomial
experiment. Explain the circumstances under which sampling without replacement could be considered
independent and, thus, binomial.

Question 51

Describe the Poisson distribution and give an example of a random variable with a Poisson distribution.

Question 52

Describe the differences in the Poisson and the binomial distribution.

Question 53

List the three methods for finding binomial probabilities in the table below, and then complete the table to
discuss the advantages and disadvantages of each.

Question 54

In the month preceding this day, the author's mother made 18 phone calls in 30 days. No calls were made on 17
days, 1 call was made on 8 days, and 2 calls were made on 5 days. Use the Poisson distribution to find the
probability of no calls in a day. Based on this probability, how many of the 30 days are expected to have no
calls?

Question 55

The pH level in a shampoo

A) Discrete
B) Continuous

Question 56

Reader's Digest ran a sweepstakes in which prizes were listed along with chances of winning: $1,000,000 (1
chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5000 (1 chance in
36,667,000), and $2500 (1 chance in 27,500,000). Assuming that there is no cost of entering the sweepstakes, find
the expected value of the amount won for one entry. If the cost of entering the sweepstakes is the cost of a
postage stamp, is it worth entering the contest?

Question 57

The number of oil spills occurring off the Alaskan coast

A) Discrete
B) Continuous

Question 58

State the requirements to use the Poisson distribution as an approximation to the binomial distribution,
including the mean for the Poisson distribution as an approximation to the binomial.

Question 59

For the table shown below, the random variable x is the number of males with tinnitus (ringing ears) among
four randomly selected males, based on a medical journal. Does the table describe a probability distribution?
Why or why not?

Question 60

In a recent U.S. Open tennis tournament, among 20 of the calls challenged by the players, 8 were overturned
after a review using an electronic system. Assume that when players challenge calls, they are successful in
having them overturned 50% of the time. The probability that among 20 challenges, 8 or fewer are overturned is
0.252. Does this result suggest that the success rate is less than 50%? Why or why not?

Question 61

Question 62

If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is
as described in the accompanying table.

Question 63

The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows.

Question 64

The height of a randomly selected student

A) Discrete
B) Continuous

Question 65

The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4096, 0.4096, 0.1536, 0.0256, and 0.0016, respectively. Round answer to the nearest hundredth.

Question 66

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled.

Question 67

The number of golf balls ordered by customers of a pro shop has the following probability distribution.

Question 68

Question 69

Provide an appropriate response. Round to the nearest hundredth.
Find the standard deviation for the given probability distribution.

Question 70

Question 71

In a certain town, 40% of adults have a college degree. The accompanying table describes the probability
distribution for the number of adults (among 4 randomly selected adults) who have a college degree.

Question 72

Question 73

The number of field goals kicked in a football game

A) Continuous
B) Discrete

Question 74

A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day
are 0.122, 0.257, 0.270, 0.189, and 0.099, respectively.

Question 75

The number of phone calls between New York and California on Thanksgiving day

A) Continuous
B) Discrete

Question 76

Question 77

In a certain town, 30% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree.

Question 78

The number of freshmen in the required course, English 101

A) Continuous
B) Discrete

Question 79

The braking time of a car

A) Discrete
B) Continuous

Question 80

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.54, 0.43, 0.02, and 0.01, respectively.