Question 1

i. For a binomial distribution, each trial has a known number of successes. For example, a four question multiple-choice test can only have zero, one, two, three and four successes (number correct). 
ii. To construct a binomial probability distribution, the number of trials and the probability of success must be known.
Iii) A binomial distribution has a characteristic that the trials are independent, which means that the outcome of one trial does not affect the outcome of any other trial.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

(i), (ii), and (iii) are all correct statements because they accurately describe the characteristics of a binomial distribution.

Question 2

Which of the following is NOT a characteristic of a binomial probability distribution?
A) Each outcome is mutually exclusive
B) Each trial is independent
C) Probability of success remains constant from trial to trial
D) Each outcome results from two trials
E) All of the choices are correct are characteristics of the binomial distribution

Accepted Answer

A binomial probability distribution involves a fixed number of independent trials, each with two possible outcomes (success or failure), not two trials.

Question 3

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?
A) 0.114
B) 0.887
C) 0.400
D) 0.231
E) None of the choices are correct

Accepted Answer

The probability can be calculated using the binomial probability formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)), where n=20, k=8, and p=0.3. This calculation results in approximately 0.114.

Question 4

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high- speed machine are defective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be defective?
A) 0.001
B) 0.167
C) 0.735
D) 0.500
E) None of the choices are correct

Accepted Answer

The probability of selecting zero defective keyboards out of six is calculated using the binomial probability formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)), where n=6, k=0, and p=0.05. This results in approximately 0.735.

Question 5

What must you know to develop a binomial probability distribution?
A) Probability of success
B) Number of trials
C) Number of successes
D) "a" and "b" only
E) "a" and "c" only

Accepted Answer

To develop a binomial probability distribution, you need to know the probability of success (a) and the number of trials (b). The number of successes (c) is a result of applying the binomial formula using a and b. Therefore, the correct answer is D, as it includes both a and b.

Question 6

A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
A) 0
B) 0.016
C) 0.062
D) 0.250
E) None of the choices are correct

Accepted Answer

The probability of guessing one question correctly is 0.5. For six questions, the probability is (0.5)^6 = 0.015625, which rounds to 0.016.

Question 7

Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?
A) 0.100
B) 0.031
C) 0.001
D) 0.250
E) None of the choices are correct

Accepted Answer

The probability of each child being a girl is 0.5. For five children, the probability that all are girls is (0.5)^5 = 0.03125, which is approximately 0.031.

Question 8

The information below is the number of daily emergency assists made to skiers by the volunteer ski team at Alpine Ski Lodge for the last 50 days. To explain, there were 22 days on which there were 2 emergency assists, and 9 days on which there were 3 emergency assists.  Convert this information to a probability distribution, and determine the mean number of assists per day.
A) 1.56
B) 1.7
C) 1.66
D) 1.76
E) 1.77

Accepted Answer

The answer of The information below is the number of...

Question 9

A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting three or more questions correct?
A) 5.1%
B) 0.64%
C) 0.032%
D) 5.79%
E) None of the choices are correct

Accepted Answer

The probability of getting three or more questions correct is 5.79%. This is because there are 25 possible combinations of answers, and only 5 of them result in getting three or more questions correct.

Question 10

A multiple-choice test consists of six questions, each with A-E answers. If you guess the answer to each question, how many questions can you expect to get correct?
A) 1
B) 3
C) 2
D) 1.2
E) None of the choices are correct

Accepted Answer

Each question has a 1/5 chance of being correct. For 6 questions, the expected number of correct answers is 6 * (1/5) = 1.2.

Question 11

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting three or more questions correct?
A) 15.6%
B) 31.25%
C) 50%
D) 100%
E) None of the choices are correct

Accepted Answer

The answer of A true-false test consists of five questions....

Question 12

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting all five questions correct?
A) 0%
B) 3.1%
C) 6.2%
D) 100%
E) None of the choices are correct

Accepted Answer

The probability of guessing one question correctly is 0.5. For five questions, the probability is (0.5)^5 = 0.03125, which is 3.125%, rounded to 3.1%.

Question 13

A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting four or more questions correct?
A) 5.1%
B) 0.64%
C) 0.032%
D) Less than 1%
E) None of the choices are correct

Accepted Answer

The answer of A multiple-choice test consists of five questions,...

Question 14

Let X represent the number of children in a Canadian household. The probability distribution of X is as follows:  Determine the expected number of children in a randomly selected Canadian household.
A) 2.25
B) 2.0
C) 2.5
D) 2.75
E) 3.0

Accepted Answer

The answer of Let X represent the number of children...

Question 15

Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?
A) 1,000
B) 0.186
C) 0.403
D) 0.000
E) None of the choices are correct

Accepted Answer

The problem can be solved using the binomial probability formula. With a probability of 0.6 for each receipt showing the order, the probability of 10 or more out of 15 is approximately 0.403.

Question 16

On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are to be selected at random for a special in-depth study on absenteeism. What is the probability of selecting 10 production employees at random on a hot summer day and finding that none of them are absent?
A) 0.002
B) 0.344
C) 0.599
D) 0.100
E) None of the choices are correct

Accepted Answer

The answer of On a very hot summer day, 5...

Question 17

Which is true for a binomial distribution?
A) There are three or more possible outcomes
B) Probability of success remains the same from trial to trial
C) Value of p is equal to 1.50
D) All of the choices are correct are correct
E) None of the choices are correct are correct

Accepted Answer

In a binomial distribution, there are only two possible outcomes (success or failure), and the probability of success (p) remains constant across trials.

Question 18

i. A binomial distribution has a characteristic that an outcome of an experiment is classified into one of two mutually exclusive categories (a success or a failure). 
ii. A binomial distribution has the characteristic that the probability of a success stays the same for each trial, but the probability of a failure varies from trial to trial.
iii. The mean of a binomial probability distribution can be determined by multiplying the probability of a failure by the number of trials.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

Statement (i) is correct as a binomial distribution involves two mutually exclusive outcomes. Statement (ii) is incorrect because the probability of success and failure remains constant across trials. Statement (iii) is incorrect because the mean is calculated by multiplying the probability of success by the number of trials, not the probability of failure.

Question 19

Which one of the following is NOT a condition of the binomial distribution?
A) Independent trials
B) Only two outcomes
C) Probability of success remains constant from trial to trial
D) At least 10 observations
E) None of the choices are correct

Accepted Answer

The binomial distribution does not require a minimum of 10 observations; it only requires a fixed number of trials.

Question 20

i. The mean of a binomial distribution is the product of the probability of success and the number of repetitions of the experiment. 
ii. The binomial probability distribution is always negatively skewed.
Iii) A binomial distribution has the characteristic that the probability of a success stays the same for each trial, but the probability of a failure varies from trial to trial.
A) (i), (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and, (iii) are correct statements but not (ii).
D) (ii) and, (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

The mean of a binomial distribution is indeed the product of the probability of success and the number of trials. However, a binomial distribution is not always negatively skewed; it can be symmetric or positively skewed depending on the probability of success. Also, the probability of success and failure remains constant in a binomial distribution.

Quiz 5: Discrete Probability Distributions

Which of the following is NOT a characteristic of a binomial probability distribution?

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high- speed machine are defective. What is the probability that out of six keyboards selected at random, exactly zero keyboards will be defective?

What must you know to develop a binomial probability distribution?

A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?

Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?

A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting three or more questions correct?

A multiple-choice test consists of six questions, each with A-E answers. If you guess the answer to each question, how many questions can you expect to get correct?

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting three or more questions correct?

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting all five questions correct?

A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting four or more questions correct?

Let X represent the number of children in a Canadian household. The probability distribution of X is as follows: Determine the expected number of children in a randomly selected Canadian household.

Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

Which is true for a binomial distribution?

Which one of the following is NOT a condition of the binomial distribution?