Deck 5: Discrete Probability Distributions

Question 1

Find the standard deviation, , for the binomial distribution which has the stated values of n and p . Round your answer to the nearest hundredth.
n=38 ; p=2 / 5

A)
B)
C)
D)

Answer 1

Question 2

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

Answer 2

C

Question 3

Find the mean, for the binomial distribution which has the stated values of n and p . Round answer to the nearest tenth. n=676 ; p=0.7

A)
B)
C)
D)

Answer 3

Question 4

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?

Question 5

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)0.154
B)0.00184
C)0.133
D)0.0635

Question 6

Mars, Inc. claims that 20% of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange
Candies in such groups of 100.

A)μ==20, σ 4.0
B)μ==20, σ .20
C)μ==.020, σ .20
D)μ==.20, σ 4.0

Question 7

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

A)Discrete
B)Continuous

Question 8

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

Question 9

Use the given values of n=2112, 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: 1564.1; maximum: 1603.9
D) Minimum: 1623.8; maximum: 1544.2

Question 10

Find the standard deviation, , for the binomial distribution which has the stated values of n and p . Round your answer to the nearest hundredth.
n=503 ; p=0.7

A)
B)
C)
D)

Question 11

Use the given values of n=93 and p=0.24 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: 30.56 ; maximum: 14.08
B) Minimum: 14.08 ; maximum: 30.56
C) Minimum: 18.2 ; maximum: 26.44
D) Minimum: -11.61 ; maximum: 56.25

Question 12

Assume that a procedure yields a binomial distribution with a trial repeated n = 30 times. Use the binomial probability formula to find the probability of x = 5 successes given the
Probability p = 1/5 of success on a single trial. Round to three decimal places.

A)0.172
B)0.067
C)0.198
D)0.421

Question 13

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

Question 14

The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? 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 15

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)1.5 twos
C)2.25 twos
D)3 twos

Question 16

Find the standard deviation, , for the binomial distribution which has n=48 and Round your answer to the nearest hundredth.

A)
B)
C)
D)

Question 17

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

Question 18

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

Question 19

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

Question 20

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.

A)
B)
C)
D)

Question 21

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

Question 22

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

Question 23

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)0.2 defects
D)18 defects

Question 24

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

Question 25

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

Question 26

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

Question 27

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)0.154
B)0.00184
C)0.133
D)0.0635

Question 28

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)0.828
B)0.172
C)0.377
D)0.205

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

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)0.982
B)0.913
C)0.055
D)0.985

Question 31

The Acme Candy Company claims that 60 % of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than 0.4 ounces? 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 32

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)0.00430
B)0.000358
C)0.00467
D)0.0512

Question 33

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

Question 34

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

A)Discrete
B)Continuous

Question 35

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

Question 36

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 37

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)0.005
B)0.046
C)0.048
D)0.222

Question 38

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

Question 39

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

A)
B)
C)
D)

Question 40

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

Question 41

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 42

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 43

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), $5,000 (1 chance in 36,667,000), and $2,500 (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 44

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 45

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 46

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 47

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

Question 48

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 49

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 50

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

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

A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run,
the player can expect to win 0. Consider the following game. The game costs $1 to play and
the winnings are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following
probabilities apply. What are your expected winnings? Does the game favor the player or the
owner?

Question 54

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 55

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 56

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 57

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 58

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 59

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.