Question 1

In a binomial experiment, the
A)probability of success does not change from trial to trial
B)probability of success does change from trial to trial
C)probability of success could change from trial to trial, depending on the situation under consideration
D)All of these answers are correct.

Accepted Answer

In a binomial experiment, the probability of success is assumed to remain constant from trial to trial. This is one of the key assumptions of a binomial experiment.

Question 2

The variance for the binomial probability distribution is
A)Var(x) = p(1- p)
B)Var(x) = np
C)Var(x) = n(1 - p)
D)Var(x)= np(1 - p)

Accepted Answer

The variance for the binomial probability distribution is given by Var(x) = np(1-p)

Question 3

The binomial probability distribution is used with
A)a continuous random variable
B)a discrete random variable
C)any distribution, as long as it is not normal
D)All of these answers are correct.

Accepted Answer

The binomial probability distribution is used with a discrete random variable, specifically one that has two possible outcomes (such as success/failure, heads/tails, etc.) and a fixed number of trials. It cannot be used with continuous random variables, and there is no restriction on using it with normal distributions. Therefore, the correct choice is B.

Question 4

Assume that you have a binomial experiment with p =0.5 and a sample size of 100. The expected value of this distribution is
A)0.50
B)0.30
C)50
D)Not enough information is given to answer this question.

Accepted Answer

The expected value of a binomial distribution with probability of success p and sample size n is given by E(X) = np. Therefore, E(X) = 100(0.5) = 50. Therefore, the best choice is C.

Question 5

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
A)0.2592
B)0.0142
C)0.9588
D)0.7408

Accepted Answer

This is a binomial probability problem. 
p = 0.04 (probability of a customer defaulting) 
n = 5 (sample size) 
We want to find the probability of exactly 2 customers defaulting. 
Using the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k) 
P(X = 2) = (5 choose 2) * 0.04^2 * 0.96^3 
= 0.0142 
Therefore, the probability that exactly two customers in the sample will default on their payments is 0.0142 or choice B.

Question 6

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
A)the experiment has a sequence of n identical trials
B)exactly two outcomes are possible on each trial
C)the trials are dependent
D)the probabilities of the outcomes do not change from one trial to another

Accepted Answer

The binomial probability distribution assumes that the trials are independent. Choice C states that the trials are dependent, so it is not a characteristic of an experiment where the binomial probability distribution is applicable.

Question 7

The standard deviation is the
A)variance squared
B)square root of the sum of the deviations from the mean
C)same as the expected value
D)positive square root of the variance

Accepted Answer

The standard deviation is the positive square root of the variance. The variance is the average of the squared deviations from the mean, and taking its positive square root gives the standard deviation. Option A is incorrect because the variance is the square of the standard deviation, not the other way around. Option B is incorrect because it describes the calculation of the variance, not the standard deviation. Option C is incorrect because expected value is a different concept altogether and is not the same as the standard deviation.

Question 8

Excel's BINOM.DIST function has how many inputs?
A)2
B)3
C)4
D)5

Accepted Answer

The BINOM.DIST function in Excel has 4 inputs: x (the number of successes), n (the number of trials), p (the probability of success), and cumulative (a logical value that determines whether to return the cumulative distribution function or the probability mass function). Therefore, the best choice is C, which indicates that there are 4 inputs.

Question 9

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.  The mean and the standard deviation for the number of electrical outages (respectively) are
A)2.6 and 5.77
B)0.26 and 0.577
C)3 and 0.01
D)0 and 0.8

Accepted Answer

The answer of The number of electrical outages in a...

Question 10

Excel's BINOM.DIST function can be used to compute
A)bin width for histograms
B)binomial probabilities
C)cumulative binomial probabilities
D)Both binomial probabilities and cumulative binomial probabilities are correct.

Accepted Answer

The BINOM.DIST function in Excel can be used to compute both binomial probabilities and cumulative binomial probabilities. Therefore, option D is the correct choice. It cannot be used to compute bin width for histograms.

Question 11

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a
A)uniform probability distribution
B)binomial probability distribution
C)hypergeometric probability distribution
D)normal probability distribution

Accepted Answer

A binomial probability distribution fits this description, as it represents the probability of a certain number of successes in a fixed number of independent trials with a constant probability of success. The other options (uniform, hypergeometric, and normal distributions) do not necessarily have a fixed number of trials or a constant probability of success.

Question 12

The standard deviation of a binomial distribution is
A)E(x) = pn(1 - n)
B)E(x) = np(1 - p)
C)E(x) =np
D)None of the alternative answers is correct.

Accepted Answer

The answer of The standard deviation of a binomial distribution...

Question 13

Which of the following is not a property of a binomial experiment?
A)the experiment consists of a sequence of n identical trials
B)each outcome can be referred to as a success or a failure
C)the probabilities of the two outcomes can change from one trial to the next
D)the trials are independent

Accepted Answer

In a binomial experiment, the probabilities of the two outcomes (success or failure) remain constant from one trial to the next. Changing probabilities would indicate a non-binomial process.

Question 14

If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the
A)standard normal probability density function
B)normal probability density function
C)Poisson probability function
D)binomial probability function

Accepted Answer

The binomial probability distribution is used when we have a fixed number of independent trials, and each trial has only two possible outcomes (success or failure). In this case, we have 15 independent trials with a probability of success of .02, making the binomial distribution the best option for calculating the probability of 4 successes out of 15 trials.

Question 15

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
A)0.0004
B)0.0038
C)0.10
D)0.02

Accepted Answer

This problem can be solved using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the sample size, k is the number of successes, p is the probability of success, and "n choose k" is a combination function that calculates the number of ways to choose k items from a set of n items.

In this case, n = 5, k = 2, and p = 0.02 (since 2% of parts are defective, p = 0.02 and 1-p = 0.98). Plugging these values into the formula, we get:

P(X=2) = (5 choose 2) * 0.02^2 * 0.98^3
= (10) * 0.0004 * 0.941192
≈ 0.0038

Therefore, the probability that the sample contains exactly two defective parts is 0.0038 or 0.38%. The best choice is B.

Question 16

When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if
A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Accepted Answer

Choosing TRUE for the fourth input will calculate the cumulative probability of randomly selecting a certain number of successes in a given number of trials, while choosing FALSE will calculate the probability of getting exactly that number of successes. Therefore, if a cumulative probability is desired, the best choice is TRUE.

Question 17

Which of the following is a characteristic of a binomial experiment?
A)at least 2 outcomes are possible
B)the probability of success changes from trial to trial
C)the trials are independent
D)All of these answers are correct.

Accepted Answer

The characteristic of a binomial experiment includes having only two possible outcomes (success or failure), a fixed probability of success, a fixed number of trials, and the trials being independent. The given information does not indicate a changing probability of success, but it does mention a fixed number of trials and independent trials. Therefore, the best choice is C.

Question 18

The expected value for a binomial probability distribution is
A)E(x) = pn(1- n)
B)E(x) = p(1 -0 p)
C)E(x) = np
D)E(x) = np(1- p)

Accepted Answer

The formula for the expected value of a binomial probability distribution is E(x) = np, where n is the number of trials and p is the probability of success on each trial. This can be derived by using the properties of the binomial distribution and the definition of expected value. Therefore, option C is the correct formula for the expected value of a binomial distribution.

Question 19

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?
A)0.0036
B)0.06
C)0.0554
D)0.28

Accepted Answer

We can find the probability of having exactly two successes in seven trials using the formula for binomial probability:

P(X = 2) = (7 choose 2) * 0.06^2 * (1 - 0.06)^5

where "7 choose 2" is the number of ways to choose 2 successes from 7 trials, and (1 - 0.06)^5 is the probability of having 5 failures.

Solving this, we get:

P(X = 2) = (7 choose 2) * 0.06^2 * 0.94^5 = 21 * 0.0036 * 0.735

P(X = 2) = 0.0554

Therefore, the probability of having exactly two successes in seven trials is 0.0554, which is closest to option C.

Question 20

x is a random variable with the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is
A)0.333
B)0.500
C)2.000
D)2.333

Accepted Answer

The answer of x is a random variable with the...

Quiz 5: Discrete Probability Distributions

In a binomial experiment, the

The variance for the binomial probability distribution is

The binomial probability distribution is used with

Assume that you have a binomial experiment with p =0.5 and a sample size of 100. The expected value of this distribution is

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

The standard deviation is the

Excel's BINOM.DIST function has how many inputs?

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. The mean and the standard deviation for the number of electrical outages (respectively) are

Excel's BINOM.DIST function can be used to compute

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

The standard deviation of a binomial distribution is

Which of the following is not a property of a binomial experiment?

If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of 4 successes in 15 trials, the correct probability function to use is the

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if

Which of the following is a characteristic of a binomial experiment?

The expected value for a binomial probability distribution is

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

x is a random variable with the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is