Question 1

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

Accepted Answer

The expected value for a binomial probability distribution is given by the formula E(x) = np, where n is the number of trials and p is the probability of success on each trial. Therefore, choice C is the correct answer.

Question 2

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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 3

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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 function is used in situations where there are a fixed number of trials (in this case, 15) and each trial has only two possible outcomes (in this case, success or failure). The probability of success is also given as .02, which satisfies the requirements for a binomial experiment. Therefore, the correct probability function to use is the binomial probability function.

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 is the product of the probability of success and the sample size. Therefore, the expected value in this case is E(X)=p*n=0.5*100=50. So, the answer is choice C.

Question 5

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 correct formula for variance of a binomial distribution is Var(x) = np(1-p), which matches option D.

Question 6

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. We have n=5 customers, and the probability of defaulting on a payment is p=0.04. We want to find the probability that exactly two customers default on their payments, which can be calculated using the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of customers who default on their payments, k=2, n=5, and p=0.04.

P(X=2) = (5 choose 2) * 0.04^2 * 0.96^3
        = 10 * 0.0016 * 0.884736
        = 0.0142

Therefore, the probability that exactly two customers in the sample will default on their payments is 0.0142 or approximately 1.42%. The best choice is B.

Question 7

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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 remains constant from trial to trial.

Question 8

The standard deviation of a binomial distribution is
A)E(x) = np(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 9

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 (i.e., the probability of a certain number of successes in a certain number of trials) and cumulative binomial probabilities (i.e., the probability of getting a certain number of successes or fewer in a certain number of trials). Therefore, option D is the correct choice. Option A is incorrect because bin width for histograms is not related to the BINOM.DIST function. Option B is partially correct, but it does not account for the fact that the function can compute cumulative probabilities as well. Option C is also partially correct, but it fails to mention that the function can also compute non-cumulative probabilities.

Question 10

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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, meaning that the outcome of one trial does not affect the outcome of another trial. In a dependent trial, the outcome of one trial can influence the outcome of the next trial, making the binomial distribution inappropriate.

Question 11

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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

The probability of success p = 0.06
The probability of failure q = 1 - p = 0.94
n = 7 (number of trials)
x = 2 (number of successes)

Using the binomial probability formula:
P(x=2) = (7 choose 2)(0.06)^2(0.94)^5 = 21(0.0036)(0.7351) = 0.0554

Therefore, the probability of two successes in seven trials is 0.0554 or approximately 5.54%. Choice C is the correct answer.

Question 12

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, p is the probability of a defective part, and k is the number of defective parts in the sample.

In this case, n=5, p=0.02, and we want to find P(X=2):
P(X=2) = (5 choose 2) * 0.02^2 * 0.98^3
P(X=2) = 10 * 0.0004 * 0.941192
P(X=2) = 0.0037648

Therefore, the answer is B: 0.0038.

Question 13

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is
A)20
B)16
C)4
D)2

Accepted Answer

The answer of Twenty percent of the students in a...

Question 14

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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

The description given fits the definition of a binomial probability distribution, which involves a fixed number of trials with a binary outcome (success or failure) and a constant probability of success. In this case, the sample of 2,500 people can be seen as a series of independent trials in which each individual either drinks coffee in the morning (success) or does not (failure). The number of successes (x) out of the total trials (n) is what is being measured, and the probability of success (i.e. the proportion of the population that drinks coffee in the morning) is assumed to remain constant across all trials. Therefore, the probability distribution of x follows a binomial distribution.

Question 15

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

The fourth input for the BINOM.DIST function specifies whether a cumulative probability is desired. Choosing TRUE will provide the probability of observing the specified number of successes or fewer, whereas choosing FALSE will provide the probability of getting exactly the specified number of successes.

Question 16

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is
A)20
B)12
C)3.46
D)Not enough information is given to answer this question.

Accepted Answer

The variance of a binomial distribution with parameters n and p is np(1-p). 
Here, n = 50 and p = 0.4. 
So, the variance = 50 x 0.4 x (1-0.4) = 12.

Question 17

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 18

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-Refer to Exhibit 5-7. The variance of the number of cups of coffee is
A).96
B).9798
C)1
D)2.4

Accepted Answer

The variance is the square of the standard deviation, which is 0.98. So the variance is 0.98^2 = 0.96.

Question 19

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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) must remain constant throughout the experiment. If the probabilities change from one trial to the next, it is no longer a binomial experiment. Therefore, option C is not a property of a binomial experiment.

Question 20

Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. 
-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, which is appropriate for counting the number of people who drink a certain number of cups of coffee, as opposed to measuring a continuous variable like the amount of coffee consumed.

Quiz 5: Discrete Probability Distributions

The expected value for a binomial probability distribution is

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -Which of the following is a characteristic of a binomial experiment?

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

The variance for the binomial probability 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?

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -In a binomial experiment, the

The standard deviation of a binomial distribution is

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

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

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?

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

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

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is

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

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -Refer to Exhibit 5-7. The variance of the number of cups of coffee is

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -Which of the following is not a property of a binomial experiment?

Exhibit 5-7 A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. -The binomial probability distribution is used with