Deck 5: Discrete Probability Distributions

Question 1

Which of the following variables are continuous?
I) an automobile's gas mileage
Ii) the air pressure in an automobile's spare tire
Iii) an automobile's sticker price

A) None are continuous.
B) i
C) i and ii
D) i, ii, and iii

Answer 1

C

Question 2

Construct the probability distribution for the number of heads obtained when tossing four coins. Draw a graph of the distribution.

Answer 2

Question 3

Continuous random variables are obtained from data that can be measured rather than counted.

Answer 3

True

Question 4

The following distribution is not a probability distribution because

A) values of the variable are negative.
B) a probability is negative.
C) the probability values do not add to 1.
D) the probability values are not discrete.

Question 5

Find the mean of the distribution shown below.

A) 2.20
B) 3.16
C) 3.04
D) 3.32

Question 6

A(n) __________ variable is one in which values are determined by chance.

Question 7

Find the mean of the distribution shown.

A) 0.50
B) 1.50
C) 1.27
D) 1.78

Question 8

The sum of the probabilities of all the events in the sample space of a probability distribution must equal 1.

Question 9

For the following data, construct a graph showing the probability distribution.

Question 10

Which of the following variables are discrete?
I) the depth of a submarine
Ii) the number of torpedoes on a submarine
Iii) the speed of the submarine

A) ii
B) i and iii
C) i and ii
D) i, ii, and iii

Question 11

What is the standard deviation of the following probability distribution?

A) 2.6
B) 4.7
C) 5.4
D) 3.9

Question 12

A(n) __________ probability distribution consists of the finite number of values a random variable can assume and the corresponding probabilities of the values.

Question 13

The following distribution is not a probability distribution because

A) the values of the variable are negative.
B) the probability values are not increasing.
C) the probability values do not add to 1.
D) the probability values are not discrete.

Question 14

The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph.

Question 15

Find the mean of the distribution shown below.

A) 4.45
B) 19
C) 0.25
D) 1

Question 16

Give the variance of the following distribution?

A) 1.83
B) 1.31
C) 1.25
D) 1.71

Question 17

Give the mean of the following probability distribution?

A) 0.25
B) 1.28
C) 2.85
D) 3.50

Question 18

Discrete variables have values that can be measured.

Question 19

Find the mean of the distribution shown.

A) 1.70
B) 4.00
C) 5.40
D) 6.00

Question 20

The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for this data.

Question 21

Using the probability distribution listed, the mean would be 1.6.

Question 22

If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts?

Question 23

A student takes a 6 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 4 questions correct?

A) 0.008
B) 0.025
C) 0.033
D) 0.066

Question 24

The formula for the variance of a probability distribution is __________.

Question 25

A jewelry supplier has a supply of earrings which are 10% platinum. A store owner orders five sets of earrings from the supplier. If the supplier selects the pairs of earrings at random, what is the chance that the jewelry store gets exactly two sets of platinum pairs?

A) 0.3645
B) 0.0405
C) 0.0729
D) 0.0030

Question 26

A student takes a 10-question, multiple-choice exam with three choices for each question and guesses on each question. Find the probability of guessing exactly 4 out of 10 correctly.

A) 0.772
B) 0.333
C) 0.400
D) 0.228

Question 27

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

A) 0.190
B) 0.162
C) 0.085
D) 0.218

Question 28

Find the variance for the values of n and p when the conditions for the binomial distribution are met.
N = 500, p = 0.75

A) 93.75
B) 375
C) 9.7
D) 125

Question 29

A coin is tossed five times. Find the probability of getting exactly three heads.

A) 0.125
B) 0.156
C) 0.800
D) 0.313

Question 30

A pet supplier has a stock of parakeets of which 20% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

A) 0.128
B) 0.384
C) 0.096
D) 0.024

Question 31

In a large bag of marbles, 25% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles?

A) 0.047
B) 0.141
C) 0.211
D) 0.063

Question 32

Find the mean of the distribution shown below.

A) 1.74
B) 2.24
C) 2.74
D) 3.24

Question 33

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?

A) $3.06
B) -$2.78
C) -$3.06
D) $2.78

Question 34

A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed.

A) 36
B) 18
C) 4.24
D) 6.78

Question 35

Find the mean for the values of n and p when the conditions for the binomial distribution are met.
N = 700, p = 0.45

A) 173.25
B) 315
C) 13.2
D) 385

Question 36

A multiple choice quiz consists of 50 questions, each with 4 possible answers. Find the mean for the number of correct answers, if a student guesses on each question.

A) 25.0
B) 12.5
C) 4.0
D) 46.0

Question 37

Compute the probability of X successes.
N = 4, X = 2, p = 0.55

A) 0.368
B) 0.632
C) 0.500
D) 0.55

Question 38

Find the standard deviation for the values of n and p when the conditions for the binomial distribution are met.
N = 1000, p = 0.7

A) 210
B) 700
C) 14.5
D) 300

Question 39

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. What is the mean of the data?

A) 1.37
B) 2.15
C) 1.89
D) 1.18

Question 40

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. Give the standard deviation for the probability distribution.

A) 1.46
B) 2.25
C) 1.89
D) 1.18

Question 41

If there are 20 typographical errors randomly distributed in a 250-page document, find the probability that a given page contains exactly two errors.

Question 42

Use the multinomial formula to find the probability for the situation in which n = 5, X₁ = 2, X₂ = 2, X₃ = 1, and, p₁ = 0.4, p₂ = 0.4, p₃ = 0.2.

A) 0.0768
B) 0.1152
C) 0.1536
D) 0.2304

Question 43

In a binomial experiment, the outcome of each trial will depend on the ones before it.

Question 44

In a survey, 60% of the voters support a particular referendum. If 40 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

Question 45

Use the multinomial formula and find the probability for the following data.

A) 0.057
B) 0.095
C) 0.333
D) 0.851

Question 46

Find the probability : P(5, 6)

A) 0.8333
B) 0.0006
C) 0.1606
D) 0.8394

Question 47

A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers.

A) Mean = 6.7, Variance = 2.2
B) Mean = 6.7, Variance = 1.5
C) Mean = 3.3, Variance = 2.2
D) Mean = 3.3, Variance = 1.5

Question 48

In a survey, 55% of the voters support a particular referendum. If 30 voters are chosen at random, find the mean and variance for the number of voters who support the referendum.

Question 49

The probability that a person will have 0, 1, or 2 dental checkups per year is 0.3, 0.6, and 0.1, respectively. If seven people are picked at random, what is the probability that two will have no checkups, four will have one checkup, and one will have two checkups in the next year?

A) 0.012
B) 0.018
C) 0.122
D) 0.588

Question 50

The probability that federal income tax returns will have 0, 1, or 2 errors is 0.73, 0.23, and 0.04, respectively. If 10 randomly selected returns are audited, what is the probability that eight will have no errors, two will have one error, and none will have two errors?

A) 0.043
B) 0.086
C) 0.192
D) 0.384

Question 51

A binomial distribution is the probabilities of the possible outcomes of a binomial experiment.

Question 52

A university has 10,000 students of which 45% are male and 55% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.

A) Mean = 16.5, Variance = 2.7
B) Mean = 13.5, Variance = 2.7
C) Mean = 16.5, Variance = 7.4
D) Mean = 13.5, Variance = 7.4

Question 53

Use the multinomial formula and find the probability for the following data.

A) 0.002
B) 0.012
C) 0.072
D) 0.124

Question 54

In binomial experiments, each trial can be viewed as having only two outcomes.

Question 55

The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam, what is the mean for the number of failures?

A) 138.1
B) 221.3
C) 90.7
D) 153.8

Question 56

The binomial distribution equations will not give exact probabilities for experiments in which sampling is done without replacement. In those cases, the trials are not independent.

Question 57

A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled.

A) 21.3
B) 50
C) 7.1
D) 5.9

Question 58

A school is sending 17 children to a camp. If 20% of the children in the school are first graders, and the 17 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen?

Question 59

The probability of a success remains the same for each trial in a binomial experiment.

Question 60

A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week?

A) 200
B) 198
C) 14.1
D) 138

Question 61

In the instructor's answer book for a mathematics text, 10% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2 incorrect answers for a homework set with 50 problems.

A)
B)
C)
D)

Question 62

In a batch of 100 cell phones, there are, on average, 5 defective ones. If a random sample of 30 is selected, find the probability of 2 defective ones.

A) 0.0500
B) 0.3000
C) 0.3163
D) 0.0667

Question 63

Use the multinomial formula to find the probability for the following situation.
X₁ = 2, X₂ = 1, X₃ = 3 when n = 6, p₁ = 0.3, p₂ = 0.5, p₃ = 0.2

A)
B)
C)
D)

Question 64

A bag contains 30 white marbles and 40 black marbles. If 5 marbles are chosen, what is the probability that there will be 2 white marbles and 3 black marbles?

A)
B)
C)
D)

Question 65

A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.

A) 0.125
B) 0.175
C) 0.600
D) 0.875

Question 66

The probability that a Poisson random variable X is equal to 4, where = 10, is

A)
B)
C)
D)

Question 67

On a Saturday evening in Chicago, 34% of the people go out to dinner, 18% go out to see a movie, 13% go out to a party, and 35% stay home. If five people are randomly selected on Monday morning, what is the probability that all but one went out Saturday night?

A) 0.048
B) 0.116
C) 0.181
D) 0.312

Question 68

A survey of 11 people at a bookstore showed that five had purchased a hardcover book. If seven people are selected at random, what is the probability that four of them had purchased a hardcover book?

A) 0.076
B) 0.250
C) 0.303
D) 0.606

Question 69

A school club consists of 30 male students and 13 female students. If 3 students are selected to represent the club in the student government, what is the probability 1 will be male and 2 will be female?

A) 0.333
B) 0.190
C) 0.221
D) 0.070