Deck 9: Binomial Distribution

Question 1

A local microbrewery believes it produces the best tasting dark beer in town. To make its case, seven volunteers are asked to participate in a beer tasting contest. Each volunteer is asked to taste 5 dark beers and to pick the one he/she prefers. Of the 5 dark beers, one is microbrewery's and the other 4 are national favorites. What is the probability that none of the volunteers pick the microbrewery's beer? Assume there is no taste preference for any of the beers and that chance alone determines each selection.

A) 0.0000
B) 0.1335
C) 0.3206
D) 0.2097

Answer 1

0.2097

Question 2

A local microbrewery believes it produces the best tasting dark beer in town. To make its case, seven volunteers are asked to participate in a beer tasting contest. Each volunteer is asked to taste 5 dark beers and to pick the one he/she prefers. Of the 5 dark beers, one is microbrewery's and the other 4 are national favorites. What is the probability that all 7 volunteers pick the microbrewery's beer? Assume there is no taste preference for any of the beers and that chance alone determines each selection.

A) 0.0000
B) 0.0001
C) 0.0078
D) 0.2097

Answer 2

0.0000

Question 3

A local microbrewery believes it produces the best tasting dark beer in town. To make its case, seven volunteers are asked to participate in a beer tasting contest. Each volunteer is asked to taste 5 dark beers and to pick the one he/she prefers. Of the 5 dark beers, one is microbrewery's and the other 4 are national favorites. What is the probability that exactly 3 of the volunteers don't pick the microbrewery's beer? Assume there is no taste preference for any of the beers and that chance alone determines each selection.

A) 0.0287
B) 0.0577
C) 0.1147
D) 0.1730

Answer 3

0.0287

Question 4

Suppose you gave a multiple-choice exam with 16 questions on it. Each question has 4 alternatives. What is the probability that a student who guesses at random on each of the 16 questions will score 4 or fewer correct answers? Assume that each alternative to each question is equally likely to be chosen.

A) 0.6302
B) 0.7982
C) 0.0383
D) 0.0000

Question 5

A local microbrewery believes it produces the best tasting dark beer in town. To make its case, seven volunteers are asked to participate in a beer tasting contest. Each volunteer is asked to taste 5 dark beers and to pick the one he/she prefers. Of the 5 dark beers, one is microbrewery's and the other 4 are national favorites. What is the probability that at least 5 of the volunteers pick the microbrewery's beer? Assume there is no taste preference for any of the beers and that chance alone determines each selection.

A) 0.0000
B) 0.0047
C) 0.0129
D) 0.0043

Question 6

A cat lover wants to know if cats have color vision. She teaches her cat to press a green button to obtain a food reward. She then gives the cat a choice between a green and a red button, but only rewards it when it presses the red button. Position of the button is controlled for. The cat is given several practice trials, and then tested 15 times. If the cat cannot distinguish between red and green, what is the probability that it will push the red button at least 12 times out of 15?

A) 0.0139
B) 0.0176
C) 0.0593
D) 0.0037

Question 7

Solving the binomial expansion to 4 decimal places will give more accurate values than the entries in Table B of the textbook.

A) true
B) false
C) depends on N
D) only if P = Q = 0.50

Question 8

Assuming the binomial distribution is appropriate, if N = 6 and P = 0.50, the probability of getting exactly 5 P events = _________.

A) 0.1094
B) 0.0156
C) 0.0609
D) 0.0938

Question 9

A true-false test of 20 questions is given to 10,000 students. If all the students guess on each question, how many students would you expect to get 17 or more questions correct?

A) 0.0013
B) 11
C) 13
D) 0.0011

Question 10

A local microbrewery believes it produces the best tasting dark beer in town. To make its case, seven volunteers are asked to participate in a beer tasting contest. Each volunteer is asked to taste 5 dark beers and to pick the one he/she prefers. Of the 5 dark beers, one is microbrewery's and the other 4 are national favorites. What is the probability that exactly 3 of the volunteers pick the microbrewery's beer? Assume there is no taste preference for any of the beers and that chance alone determines each selection.

A) 0.1730
B) 0.1147
C) 0.0577
D) 0.0287

Question 11

If an event has 3 possible outcomes, then one cannot use the binomial distribution in analyzing the results.

A) true
B) false
C) depends on N
D) depends on the situation

Question 12

Assuming the binomial distribution is appropriate, if N = 7, P = 0.40, what is the exact probability (7 decimal place accuracy) of getting 7 P events?

A) 0.0016000
B) 0.0016384
C) 0.0016254
D) can't tell because the binomial table only gives 4 decimal place accuracy

Question 13

Assuming the binomial distribution is appropriate, if N = 7, P = 0.40, and the number of P events = 2, the number of Q events = _________.

A) 5
B) 2
C) 0.60
D) need more information

Question 14

The binomial distribution is symmetrical _________.

A) for all values of P and Q
B) only when P = Q = .50
C) for N > 8
D) for P > Q

Question 15

The binomial expansion equals _________.

A) ( P + Q ) N
B) P + Q
C) ( P + Q ) ²
D) 1

Question 16

The requirements for the binomial distribution are _________.

A) a series of N trials
B) only two possible outcomes on each trial
C) the outcomes on each trial are mutually exclusive
D) there is independence between trials
E) all of these

Question 17

The binomial distribution _________.

A) is a probability distribution
B) gives each possible outcome of N trials
C) gives the probability of getting each outcome
D) all of these

Question 18

Assuming the binomial distribution is appropriate, if N = 12 and P = 0.60, the probability of getting exactly 11 P events is _________.

A) 0.0010
B) 0.0003
C) 0.0075
D) 0.0174

Question 19

As N increases, the binomial distribution _________.

A) becomes skewed
B) becomes more normally distributed
C) is easier to use
D) changes from a discrete to a continuous distribution

Question 20

Assuming the binomial distribution is appropriate, if N = 10 and P = 0.30, the probability of getting at least 8 P events is _________.

A) 0.1493
B) 0.1211
C) 0.0015
D) 0.0014

Question 21

What is the probability that one can call the flip of a coin correctly at least 6 out of 7 times assuming that the coin is fair?

A) 0.0078
B) 0.0547
C) 0.5000
D) 0.0625
E) 0.1250

Question 22

Assume your friend just took an exam made up of 20 true/false questions. Further assume that your friend had no knowledge relevant to the questions, and consequently just guessed the answer to each question What is the probability your friend will pass the exam. Each question has the same weight and 60% or more correct answers results in a passing grade.

A) 0.1316
B) 0.1307
C) 0.2517
D) 0.0580

Question 23

The probability of obtaining a result as extreme or more extreme than 4 heads if 11 coins were tossed and p ( H ) = 0.35 is _________.

A) 0.6683
B) 0.2745
C) 0.5490
D) 0.7184

Question 24

Assume your friend just took an exam made up of 20 true/false questions. Further assume that your friend had no knowledge relevant to the questions, and consequently just guessed the answer to each question. What is the probability he will get an A, if 90 - 100% defines the A range?

A) 0.0013
B) 0.0011
C) 0.0000
D) 0.0002

Question 25

What is the value of 6 P ₅ Q if P = 0.20?

A) 0.0003
B) 0.1600
C) 0.0469
D) 0.0015

Question 26

If P = 0.40 for the probability of getting a head on any one flip of the coin, then _________.

A) the odds of getting 4 out of 4 heads equals the odds of getting 4 out of 4 tails
B) the odds of getting a head on any one toss is greater than the odds of getting a tail
C) the odds of getting a tail is greater than the odds of getting a head
D) cannot be determined

Question 27

Consider the binomial expansion for 6 events: P ₆ + 6 P ₅ Q + 15 P ₄ Q ₂ + 20 P ₃ Q ₃ + 15 P ₂ Q ₄ + 6 PQ ₅ + Q ₆ What term(s) would you use to evaluate the probability of obtaining 1 or fewer heads from 6 flips of an unbiased coin?

A) 6 PQ ₅
B) 6 PQ ₅ + Q ₆
C) Q ₆
D) 20 P ₃ Q ₃

Question 28

P 0 equals _________.

A) 1.00
B) 0.00
C) 0.50
D) Q

Question 29

If Q = 0.30 then P equals _________.

A) 0.30
B) 0.90
C) 0.70
D) 0.10

Question 30

If one flips 5 unbiased coins once, what is the probability of getting exactly 3 heads?

A) 0.6000
B) 0.3125
C) 0.4687
D) 0.0312

Question 31

In one flip of 10 unbiased coins, what is the probability of getting a result as extreme or more extreme than 8 heads?

A) 0.0547
B) 0.1094
C) 0.0020
D) 1.0000

Question 32

What is the probability of obtaining exactly 5 P events if the appropriate term of the binomial expansion to evaluate were 6 P 5 Q 1 and P = 0.42?

A) 0.0784
B) 0.0455
C) 0.4616
D) 0.0076

Question 33

A football player is practicing making field goals from the 30-yard line. If the probability of his kicking a field goal is 0.75, what is the probability he will kick at least 12 field goals in the next 15 tries? Assume independence between tries.

A) 0.0000
B) 0.2252
C) 0.4613
D) 0.6481

Question 34

What is the probability of 4 heads turning up out of four tosses of the coin if the probability of any one head is P = 0.40?

A) 0.0625
B) 0.1296
C) 0.0256
D) 0.3456

Question 35

In the binomial expansion of ( P + Q ) 10 , the last term of the expansion will be _________.

A) Q 10
B) P 10
C) P 10 + Q 10
D) depends on the values of P and Q

Question 36

Consider the binomial expansion for 6 events: P ₆ + 6 P ₅ Q + 15 P ₄ Q ₂ + 20 P ₃ Q ₃ + 15 P ₂ Q ₄ + 6 PQ ₅ + Q ₆ What term would you use in evaluating the probability of obtaining exactly 2 heads as the result of flipping an unbiased coin 6 times?

A) P ₆
B) 20 P ₃ Q ₃
C) 15 P ₂ Q ₄
D) the entire expression

Question 37

In order to use the binomial distribution, which of the following conditions are necessary?

A) a series of N trials with only 2 possible outcomes
B) outcomes are mutually exclusive
C) there must be independence between trials
D) P and Q must remain the same from trial to trial.
E) all of these

Question 38

If one of the terms in a binomial expansion were 210 P 6 Q 4 , what is the value of N ?

A) 210
B) 6
C) 4
D) 10

Question 39

The sum of all terms in any binomial expansion will equal _______.

A) 1.0000
B) 0.5000
C) depends on the values of P and Q
D) 0.0000 (WWW)

Question 40

In one flip of 10 unbiased coins, what is the probability of getting 8 or more heads?

A) 0.0547
B) 0.0016
C) 0.0439
D) 0.0010

Question 41

Assume your friend just took an exam made up of 20 true/false questions. Further assume that your friend had no knowledge relevant to the questions, and consequently just guessed the answer to each question. What is the probability your friend will fail the exam, if a failing grade is 59% or below?

A) 0.8686
B) 0.8684
C) 0.8693
D) 0.7483

Question 42

Teresa, a star player in women's college softball, is participating in a home run contest. If the probability she will hit a home run on any pitch is 0.65 what is the probability that out of 10 tries, at least 7 will be home runs?

A) 0.5139
B) 0.0260
C) 0.0719
D) 0.6496

Question 43

In a situation where there are only two possible events, A and B, on each trial, if P = Q on each trial

A) A and B are necessarily independent
B) A and B are necessarily dependent
C) p (A) must be greater than p(B)
D) A and B must be mutually exclusive
E) a and d

Question 44

The binomial distribution only applies to situations where P = 0.50.

Question 45

Your introductory psychology class has 189 males and 261 females. If you randomly sample 40 of these classmates, what is the probability you will get at least 32 females?

A) 0.0049
B) 0.0025
C) 0.0048
D) 0.0024

Question 46

In solving a binomial problem, if the evaluation required only finding the probability of all P events, and N = 40, evaluating P ⁴⁰ would be more accurate than using the normal approximation. Assume no rounding.

A) T
B) F
C) It depends on the value of P
D) if P = Q = .50, the normal approximation would be more accurate.

Question 47

Evaluated over a large number of pitches, a varsity women softball pitcher threw 1400 strikes and 600 balls. Assuming things remain the same, what is the probability she will throw at least 35 strikes in her next 40 pitches. Assume independence between throws.

A) 0.0427
B) 0.0418
C) 0.0001
D) 0.0078

Question 48

The binomial distribution is _________ symmetrical.

A) always symmetrical
B) sometimes symmetrical, depending on the values of P and Q
C) always symmetrical if N is over 30
D) b and c

Question 49

Assume your friend just took an exam made up of 20 true/false questions. Further assume that your friend had no knowledge relevant to the questions, and consequently just guessed the answer to each question. What is the probability he will get a B, if the B range is 80-89%?

A) 0.0059
B) 0.0057
C) 0.0046
D) 0.0011

Question 50

For the binomial distribution to be appropriate, P and Q must be equal.

Question 51

Suppose you flip 35 biased coins once. The probability of a head with each coin equals 0.30. What is the probability you will get 15 or more heads?

A) 0.0485
B) 0.0446
C) 0.0495
D) 0.0548

Question 52

Assume you are flipping an unbiased coin and that the flipping process is entirely random. A psychic claims that he can sense the outcome of each flip. You put him to the test. You flip the coin 6 times and guess what? The psychic correctly calls the outcome each time. If the psychic is really only guessing on each flip, what is the probability of his being correct six out of six times?

A) 0.1094
B) 0.0041
C) 0.0156
D) 0.0083

Question 53

The binomial distribution is a discrete distribution.

Question 54

A biased coin is defined as _________.

A) a coin that when tossed always comes up heads
B) a coin that when tossed has a probability of coming up heads that is equal to the probability of coming up tails
C) a coin that when tossed has a probability of coming up heads that is unequal to the probability of coming up tails
D) a coin that when tossed always comes up tails
E) a, c, and d

Question 55

P + Q = 1.

Question 56

The binomial distribution only applies to flipping coins and not to real life situations.

Question 57

The binomial distribution is always symmetrical.

Question 58

The binomial distribution can be used when there are three outcomes on each trial.

Question 59

For the binomial distribution to be applicable to a situation,

A) the value of P and Q must be the same from trial-to-trial
B) the number of trials should be small
C) the outcome of one trial can affect the value of P or Q of another trial
D) none of the above

Question 60

The binomial distribution requires that the P and Q do not change from trial-to-trial.

Question 61

You are solving a binomial problem with N = 25, It is theoretically and practically possible to solve the problem using the binomial expansion.

Question 62

It is preferable to use the normal approximation because it is more accurate than the binomial table.

Question 63

To apply the binomial distribution properly ( P + Q ) must equal 1.00.

Question 64

If P > Q , the binomial distribution will be symmetrical.

Question 65

Because Table B, "Binomial Distribution," in Appendix D of the textbook only lists probabilities for values of P = 0.40 and 0.45, it is not possible to use the binomial distribution to solve problems where P = 0.43.

Question 66

A valid example of a situation where one can apply the binomial distribution is in determining the probability of rolling a 6 or a 5 with the toss of a pair of dice.

Question 67

In ( P + Q ) 7 the term Q 7 indicates 0 P events.

Question 68

The binomial distribution requires that P and Q stay the same from trial-to-trial.

Question 69

In order to correctly apply the binomial distribution, one of the conditions that must be met is that there are only two possible outcomes on each trial.

Question 70

To apply the binomial distribution, three of the conditions which must be met are that there is a series of N trials where the outcomes are mutually exclusive and there is independence between trials.

Question 71

If P = 0.30 and Q = 0.67, the binomial distribution does not apply.

Question 72

The binomial distribution applies equally well to discrete and continuous variables.

Question 73

( P + Q ) 2 = P 2 + Q 2 in the binomial expansion.

Question 74

For the binomial distribution to apply to any situation, the situation must involve only two possible outcomes on each trial.

Question 75

The probability of 7 P events when N = 10 and P = 0.8 is the same as 3 Q events if Q = 0.2 and N = 10.

Question 76

One can appropriately apply the binomial distribution if P = 0.5 and Q = 0.3 in a problem.

Question 77

The requirement that NP ?5= 10 is a necessary and sufficient requirement for using the normal approximation.

Question 78

If P ≠ Q , the binomial distribution will still be normally distributed.

Question 79

In ( P + Q ) 6 the term Q 6 indicates 0 P events.

Question 80

One can appropriately apply the binomial distribution if P = 0.37 and Q = 0.63.