A company uses three different assembly lines— A 1 , A 2 and A 3 —to manufacture a particular component. Of those manufactured by A 1 , 5% need rework to remedy a defect, whereas 8% of A 2 ’s components and 10% of A 3 ’s components need rework. Suppose that 50% of all components are produced by A 1 , 30% are produced by A 2 and 20% are produced by A 3 . a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches. b. What is the probability that a randomly selected component came from A 1 and needed rework? c. What is the probability that a randomly selected component needed rework?

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 6, Problem 87CR

A company uses three different assembly lines—A₁, A₂ and A₃—to manufacture a particular component. Of those manufactured by A₁, 5% need rework to remedy a defect, whereas 8% of A₂’s components and 10% of A₃’s components need rework. Suppose that 50% of all components are produced by A₁, 30% are produced by A₂ and 20% are produced by A₃.

a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
b. What is the probability that a randomly selected component came from A₁ and needed rework?
c. What is the probability that a randomly selected component needed rework?

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO

Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?

A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

Answer 2

Textbook Question

Chapter 6, Problem 87CR

A company uses three different assembly lines—A₁, A₂ and A₃—to manufacture a particular component. Of those manufactured by A₁, 5% need rework to remedy a defect, whereas 8% of A₂’s components and 10% of A₃’s components need rework. Suppose that 50% of all components are produced by A₁, 30% are produced by A₂ and 20% are produced by A₃.

a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
b. What is the probability that a randomly selected component came from A₁ and needed rework?
c. What is the probability that a randomly selected component needed rework?

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 6, Problem 87CR

A company uses three different assembly lines—A₁, A₂ and A₃—to manufacture a particular component. Of those manufactured by A₁, 5% need rework to remedy a defect, whereas 8% of A₂’s components and 10% of A₃’s components need rework. Suppose that 50% of all components are produced by A₁, 30% are produced by A₂ and 20% are produced by A₃.

a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
b. What is the probability that a randomly selected component came from A₁ and needed rework?
c. What is the probability that a randomly selected component needed rework?

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 6, Problem 87CR

A company uses three different assembly lines—A₁, A₂ and A₃—to manufacture a particular component. Of those manufactured by A₁, 5% need rework to remedy a defect, whereas 8% of A₂’s components and 10% of A₃’s components need rework. Suppose that 50% of all components are produced by A₁, 30% are produced by A₂ and 20% are produced by A₃.

a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
b. What is the probability that a randomly selected component came from A₁ and needed rework?
c. What is the probability that a randomly selected component needed rework?

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Answer 8

a.

Expert Solution

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Draw a tree diagram with first-generation branches corresponds to the three lines.

Answer 13

Answer to Problem 87CR

The tree diagram with first-generation branches corresponds to the three lines is:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 1

Answer 14

Explanation of Solution

Calculation:

The given information is that about 50% of component manufactured by A1 among that 5% need rework to remedy a defect, about 30% of component manufactured by A2 among that 8% need rework to remedy a defect and about 20% of component manufactured by A3 among that 10% need rework to remedy a defect.

Here, the probability of component manufactured by A1 is 0.5.

The probability of component manufactured by A2 is 0.3.

The probability of component manufactured by A3 is 0.2.

The probability of component manufactured by A1, need rework to remedy a defect is 0.05.

The probability of component manufactured by A2, need rework to remedy a defect is 0.08.

The probability of component manufactured by A3, need rework to remedy a defect is 0.1.

Tree diagram:

Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.

The following tree diagram represents the given situation:

Introduction to Statistics and Data Analysis, Chapter 6, Problem 87CR , additional homework tip 2

Answer 15

b.

Expert Solution

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Compute the probability that a randomly selected component came from A1 and needed rework.

Answer 20

Answer to Problem 87CR

The probability that a randomly selected component came from A1 and needed rework is 0.025.

Answer 21

Explanation of Solution

Calculation:

The probability that a randomly selected component came from A1 and needed rework is calculated as follows:

P(A1∩R)=(0.5)×(0.05)=0.025

Thus, the probability that a randomly selected component came from A1 and needed rework is 0.025.

Answer 22

c.

Expert Solution

To determine

Find the probability that a randomly selected component need rework.

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Find the probability that a randomly selected component need rework.

Answer 27

Answer to Problem 87CR

The probability that a randomly selected component need rework is 0.069.

Answer 28

Explanation of Solution

Calculation:

The probability that a randomly selected component need rework is calculated as follows:

P(R)=(0.5)(0.05)+(0.3)(0.08)+(0.2)(0.1)=0.025+0.024+0.02=0.069

Thus, the probability that a randomly selected component need rework is 0.069.

Answer 29

Ch. 6.1 - Define the term chance experiment, and give an...Ch. 6.1 - Define the term sample space, and then give the...Ch. 6.1 - Consider the chance experiment in which the type...Ch. 6.1 - A tennis shop sells five different brands of...Ch. 6.1 - A new model of laptop computer can be ordered with...Ch. 6.1 - A college library has four copies of a certain...Ch. 6.1 - A library has five copies of a certain textbook on...Ch. 6.1 - Suppose that, starting at a certain time,...Ch. 6.1 - Refer to the previous exercise and now suppose...Ch. 6.1 - Prob. 10E

Solution Summary: The author explains that a tree diagram with first-generation branches corresponds to the three lines. The probability of component manufactured by A_1 and needed rework is 0.05.

Concept explainers

Videos

Answer to Problem 87CR

Explanation of Solution

Answer to Problem 87CR

Explanation of Solution

Answer to Problem 87CR

Explanation of Solution

Want to see more full solutions like this?

Chapter 6 Solutions