Question 1

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-2. What is the probability that among the students in the sample exactly two are female?
A)0.0896
B)0.2936
C)0.0413
D)0.0007

Accepted Answer

The answer of Exhibit 5-2
The student body of a large...

Question 2

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 7 are female?
A)0.1064
B)0.0896
C)0.0168
D)0.8936

Accepted Answer

The answer of Exhibit 5-2
The student body of a large...

Question 3

Exhibit 5-5
Probability Distribution
 
-Refer to Exhibit 5-5. The expected value of x equals
A)24
B)25
C)30
D)100

Accepted Answer

The answer of Exhibit 5-5
Probability Distribution
 
-Refer to Exhibit 5-5....

Question 4

Exhibit 5-2
The student body of a large university consists of 60% female students. A random sample of 8 students is selected.
-Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 6 are male?
A)0.0413
B)0.0079
C)0.0007
D)0.0499

Accepted Answer

To solve this problem, we will use the binomial distribution formula:
P(X≥6) = 1 - P(X<6)
where X is the number of male students in the sample, and P(X<6) is the probability that there are less than 6 male students in the sample.
We can calculate P(X<6) using the binomial probability formula:
P(X<6) = Σ(i=0 to 5) (8 choose i) (0.4)^i (0.6)^(8-i)
where (8 choose i) is the binomial coefficient that represents the number of ways to choose i male students out of 8, and (0.4)^i (0.6)^(8-i) is the probability of getting i male students and 8-i female students.
Using a calculator or software, we can find that P(X<6) = 0.9501.
Therefore, P(X≥6) = 1 - P(X<6) = 0.0499, which is answer choice D.

Question 5

Exhibit 5-6
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 5-6. The expected number of cups of coffee is
A)1
B)1.2
C)1.5
D)1.7

Accepted Answer

To find the expected number of cups of coffee, we need to calculate the mean of the sample. Using the formula for sample mean, we get:

Mean = (sum of all observations) / (sample size)
Mean = (1020 + 866 + 642 + 526 + 416 + 407 + 205 + 74) / 2500
Mean = 3156 / 2500
Mean = 1.26

So the expected number of cups of coffee is 1.2, which corresponds to choice B.

Question 6

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is
A).008
B).096
C).104
D).8

Accepted Answer

The answer of Exhibit 5-7
The probability that Pete will catch...

Question 7

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
 
-Refer to Exhibit 5-3. The standard deviation is
A)1.431
B)2.047
C)3.05
D)21

Accepted Answer

The answer of Exhibit 5-3
Roth is a computer-consulting firm. The...

Question 8

Exhibit 5-5
Probability Distribution
 
-Refer to Exhibit 5-5. The variance of x equals
A)9.165
B)84
C)85
D)93.33

Accepted Answer

The answer of Exhibit 5-5
Probability Distribution
 
-Refer to Exhibit 5-5....

Question 9

Exhibit 5-4
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
-Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is
A)0.0778
B)0.7780
C)0.5000
D)0.3456

Accepted Answer

This is a binomial probability problem with n=5 and p=0.40. Using the binomial probability formula, we can find the probability of getting exactly 2 female voters:
P(X=2) = (5 choose 2) * (0.40)^2 * (1-0.40)^3
P(X=2) = 10 * 0.16 * 0.216
P(X=2) = 0.3456
Therefore, the correct answer is D)0.3456.

Question 10

Exhibit 5-1
The following represents the probability distribution for the daily demand of computers at a local store.
 
-Refer to Exhibit 5-1. The expected daily demand is
A)1.0
B)2.2
C)2, since it has the highest probability
D)of course 4, since it is the largest demand level

Accepted Answer

The expected daily demand can be calculated by summing the product of each demand level and its corresponding probability. In this case, (0.1 x 0) + (0.3 x 1) + (0.2 x 2) + (0.2 x 3) + (0.1 x 4) = 2.2, so the correct answer is B.

Question 11

Exhibit 5-1
The following represents the probability distribution for the daily demand of computers at a local store.
 
-Refer to Exhibit 5-1. The probability of having a demand for at least two computers is
A)0.7
B)0.3
C)0.4
D)1.0

Accepted Answer

To find the probability of demand for at least two computers, we need to add the probabilities of demand for 2, 3, or 4 computers. So, P(demand for at least two computers) = P(2) + P(3) + P(4) = 0.2 + 0.3 + 0.2 = 0.7. Therefore, the answer is A.

Question 12

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is
A).008
B).096
C).104
D).8

Accepted Answer

The answer of Exhibit 5-7
The probability that Pete will catch...

Question 13

Exhibit 5-4
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.
-Refer to Exhibit 5-4. The probability that there are no females in the sample is
A)0.0778
B)0.7780
C)0.5000
D)0.3456

Accepted Answer

The answer of Exhibit 5-4
Forty percent of all registered voters...

Question 14

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)0.0600
C)0.0555
D)0.2800

Accepted Answer

We use the formula for binomial probability:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, p is the probability of success, and k is the number of successes we want to find.

In this case, n=7, p=0.06, and k=2. Plugging in the values, we get:
P(X=2) = (7 choose 2) * 0.06^2 * 0.94^5
P(X=2) = 21 * 0.0036 * 0.7351
P(X=2) = 0.0555

Therefore, the probability of two successes in seven trials is 0.0555 or choice C.

Question 15

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
 
-Refer to Exhibit 5-3. The variance is
A)1.431
B)2.047
C)3.05
D)21

Accepted Answer

To find the variance, we need to calculate the expected value, which is the sum of the product of each possible outcome and its probability.

Expected value = (0 x 0.22) + (1 x 0.28) + (2 x 0.20) + (3 x 0.15) + (4 x 0.10) + (5 x 0.03) + (6 x 0.02)
Expected value = 1.64

Now we can calculate the variance by taking the sum of the squared difference between each possible outcome and the expected value, weighted by its probability.

Variance = [(0-1.64)^2 x 0.22] + [(1-1.64)^2 x 0.28] + [(2-1.64)^2 x 0.20] + [(3-1.64)^2 x 0.15] + [(4-1.64)^2 x 0.10] + [(5-1.64)^2 x 0.03] + [(6-1.64)^2 x 0.02]
Variance = 2.047

Therefore, the answer is B) 2.047.

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)144

Accepted Answer

The variance of a binomial distribution is calculated as np(1-p), where n is the sample size and p is the probability of success. Thus, in this case, the variance would be 50(0.4)(0.6) = 12. Therefore, the best choice is B.

Question 17

Exhibit 5-6
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 5-6. The variance of the number of cups of coffee is
A).96
B).9798
C)1
D)2.4

Accepted Answer

The answer of Exhibit 5-6
A sample of 2,500 people was...

Question 18

A random variable that may take on any value in an interval or collection of intervals is known as a
A)continuous random variable
B)discrete random variable
C)continuous probability function
D)finite probability function

Accepted Answer

A continuous random variable is one that can take any value within a given range of values, meaning there are infinite possible values. This is in contrast to a discrete random variable, which can only take on specific values. Continuous probability functions are also associated with continuous random variables. A finite probability function would not apply in this case, as it only takes on a finite number of values.

Question 19

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
 
-Refer to Exhibit 5-3. The expected number of new clients per month is
A)6
B)0
C)3.05
D)21

Accepted Answer

The expected value (mean) is calculated by taking the sum of the products of each possible outcome and its probability. 
E(X) = (0 x 0.10) + (1 x 0.15) + (2 x 0.25) + (3 x 0.30) + (4 x 0.15) + (5 x 0.05) + (6 x 0.05) = 3.05. Therefore, the expected number of new clients per month is 3.05.

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

Exhibit 5-2 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-2. What is the probability that among the students in the sample exactly two are female?

Exhibit 5-2 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 7 are female?

Exhibit 5-5 Probability Distribution -Refer to Exhibit 5-5. The expected value of x equals

Exhibit 5-2 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 6 are male?

Exhibit 5-6 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 5-6. The expected number of cups of coffee is

Exhibit 5-7 The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. -Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is

Exhibit 5-3 Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. -Refer to Exhibit 5-3. The standard deviation is

Exhibit 5-5 Probability Distribution -Refer to Exhibit 5-5. The variance of x equals

Exhibit 5-4 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. -Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is

Exhibit 5-1 The following represents the probability distribution for the daily demand of computers at a local store. -Refer to Exhibit 5-1. The expected daily demand is

Exhibit 5-1 The following represents the probability distribution for the daily demand of computers at a local store. -Refer to Exhibit 5-1. The probability of having a demand for at least two computers is

Exhibit 5-7 The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. -Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is

Exhibit 5-4 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. -Refer to Exhibit 5-4. The probability that there are no females in the sample is

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

Exhibit 5-3 Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. -Refer to Exhibit 5-3. The variance is

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

Exhibit 5-6 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 5-6. The variance of the number of cups of coffee is

A random variable that may take on any value in an interval or collection of intervals is known as a

Exhibit 5-3 Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. -Refer to Exhibit 5-3. The expected number of new clients per month is

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