Deck 4: Discrete Probability Distributions

Question 1

When sampling is done without replacement, the binomial distribution does not give exact probabilities
because the trials are not independent.

Answer 1

True

Question 2

In a binomial experiment, the outcomes of each trial must be dependent on each other.

Answer 2

False

Question 3

The outcomes of a binomial experiment and the corresponding probabilities of these outcomes are called
a binomial distribution.

Answer 3

True

Question 4

Question 5

If the standard deviation of a probability distribution is 1.71, the variance is 1.31.

Question 6

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

Question 7

The probability of observing 50 heads in 100 tosses of a fair coin is less likely than observing 500 heads
in 1000 tosses.

Question 8

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

Question 9

Discrete variables have values that can be measured.

Question 10

If the standard deviation of a probability distribution is 6.25, the variance is 2.30.

Question 11

A) A values of x is negative
B) A probability is negative
C) The probability values do not add to 1
D) The probability values are not discrete

Question 12

A) The values of x 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 13

By computing the binomial mean and variance and using the empirical rule, one finds that the probability
of obtaining between 40 and 60 heads in 100 tosses of a fair coin is approximately 95%.

Question 14

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

Question 15

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

Question 16

A) 0.12
B) 0.24
C) 0.41
D) 0.76

Question 17

The Poisson distribution is used when n is small and p is large.

Question 18

A) 0.15
B) 0.25
C) 0.10
D) There is no value that would make this a probability distribution

Question 19

In a multinomial distribution, events must be mutually exclusive.

Question 20

In binomial experiments, the outcomes are usually classified as successes or failures.

Question 21

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) 0.19
B) 0.17
C) 0.08
D) 0.23

Question 22

A pet supplier has a stock of parakeets of which 10% 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) 0.081
B) 0.243
C) 0.027
D) 0.003

Question 23

A) 0.79
B) 1.25
C) 1.01
D) 1.52

Question 24

A) 0.12
B) 0.24
C) 0.48
D) There is no value that would make this a probability distribution

Question 25

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 26

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

A) 0.3750
B) 0.1563
C) 0.2500
D) 0.3125

Question 27

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

Question 28

A) -0.98
B) 0.50
C) 1.34
D) -0.02

Question 29

A) 1.52
B) 2.02
C) 2.52
D) 3.02

Question 30

In a large bag of marbles, 40% 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 one three red marbles?

A) 0.1536
B) 0.2304
C) 0.3456
D) 0.1920

Question 31

Give the mean of the following probability distribution?

A) 1.20
B) 1.46
C) 3.15
D) 2.13

Question 32

A) 1.72
B) 4.00
C) 5.44
D) 6.00

Question 33

What is the standard deviation of the following probability distribution?

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

Question 34

Question 35

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

Question 36

A) -1.89
B) -1.58
C) -2.10
D) 2.10

Question 37

What of the following pairs of probability values would complete the following probability distribution?

Question 38

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

Question 39

A) 1.00
B) 1.84
C) 2.32
D) 2.68

Question 40

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 41

A) 0.057
B) 0.224
C) 0.014
D) 0.022

Question 42

The probability that federal income tax returns will have 0, 1, or 2 errors is 0.53, 0.15, and 0.32, respectively. If 10 randomly selected returns are audited, what is the probability that six will have no
Errors, three will have one error, and one will have two errors?

A) 0.184
B) 0.127
C) 0.020
D) 0.035

Question 43

Question 44

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 45

The supervisor at a large plant estimates that there are defective parts about 1% of the time. If the plant produces 20,000 parts in a week, what is the variance for the number of defective parts?

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

Question 46

In the Selected

Question 47

A bag contains 25 white marbles and 32 black marbles. The probability P(X) of selecting without replacement a sample of size 9 of 3 white marbles and 6 black marbles is

Question 48

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

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

Question 49

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

A) 60
B) 50
C) 7.1
D) 4.3

Question 50

A multiple choice quiz consists of 7 questions, each with 3 possible answers. If a student guesses at the answer to each question, then the mean number of correct answers is

A) 7.00
B) 2.33
C) 3.00
D) 10.00

Question 51

Question 52

The probability that a Poisson random variable X is equal to 2, where = 7, is

Question 53

A university has 10,000 students of which 3000 are male and 7000 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 = 12, Variance = 12
B) Mean = 9, Variance = 6.3
C) Mean = 6, Variance = 1.8
D) Mean = 6.3, Variance = 9

Question 54

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will
Not be sold if there are actually three dead batteries in the package?

Question 55

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

A) 138.1
B) 171.2
C) 90.7
D) 153.8

Question 56

Using the multinomial formula, find the probability of the following data.

A) 0.728
B) 0.032
C) 0.013
D) 0.325

Question 57

On a Saturday evening, 34% of the people in Winnipeg go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. If seven people are randomly selected, what is the probability that one eats
Out, three see a movie, two have a party, and one stays at home?

A) 0.099
B) 0.459
C) 0.102
D) 0.0049

Question 58

A computer store has 50 printers of which 40 are laser printers and 10 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 = 2, Variance = 0.2
B) Mean = 2, Variance = 3
C) Mean = 1, Variance = 0.2
D) Mean = 2, Variance = 1.6

Question 59

The probability that a person will have 0, 1, or 2 dental checkups per year is 0.2, 0.5, and 0.3, 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) 0.079
B) 0.013
C) 0.008
D) 0.043

Question 60

A survey of 12 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?

Question 61

Question 62

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

Question 63

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

Question 64

Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!)

A) 0.25
B) 0.50
C) 0.75
D) 1.00

Question 65

If a trial in an experiment has more than two outcomes, a(n) __________ distribution must be used.
________________________________________

Question 66

Which of the following would be a measure of spread of a probability distribution.

Question 67

The mean, variance, and standard deviation should be rounded to one more decimal place than the
outcome, X.

Question 68

The __________ is a distribution of a variable that has two outcomes when sampling is done without
replacement.
________________________________________

Question 69

A school is sending 9 children to a camp. If 15% of the children in the school are first graders, and the 8
children are selected at random, what is the mean and variance of the number of first graders chosen?

Question 70

Question 71

One of the requirements for a binomial experiment is that there must be a __________ number of
trials.
________________________________________

Question 72

Draw a graph showing the probability distribution for the sample space for tossing four coins.

Question 73

A club consists of 4 male students and 6 female students. The probability P(X) of selecting without replacement a sample of size 4 of 2 male students and 2 female students is

Question 74

In a survey, 65% of the voters support a particular referendum. If 40 voters are chosen at random, and X
is the number of voters that support this referendum, find the standard deviation of X.

Question 75

Question 76

In a survey, 80% of the voters support a particular referendum. If 40 voters are chosen at random, and X
is the number of voters that support this referendum, find the mean and variance of X.

Question 77

The __________ of a discrete random variable of a probability distribution is the theoretical average of
the variable.
________________________________________

Question 78

Which of the following could be used as a measure of spread of a probability distribution.

Question 79

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?