To test: Whether the area under the curve is 1 or not.

Question

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Answer 1

Question

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

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Answer 2

Question

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

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Answer 3

Question

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

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Answer 4

Question

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

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Answer 5

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Answer 6

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

Answer 7

Chapter 4.3, Problem 60E

(a)

To determine

To test: Whether the area under the curve is 1 or not.

Answer 8

(a)

Expert Solution

Answer to Problem 60E

Solution: Yes, the area under the curve is 1.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation: The area of a triangle is,

Area=12×base×height

The height is 1 and the base is equal to 2. Thus, the area can be calculated as:

Area=12×base×height=12×2×1=1

Hence, the area is 1. The provided curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 1

Answer 13

(b)

Section 1:

To determine

To find: The probability P(Y<1).

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Answer 14

(b)

Section 1:

To determine

To find: The probability P(Y<1).

Answer 15

(b)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.5.

Answer 16

(b)

Section 1:

Expert Solution

Answer 17

(b)

Section 1:

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,1]. Thus, from the provided triangle, base is 1 and height is equal to 1 because the triangle is symmetrical about its vertical line. Thus, the area can be calculated by the formula:

Area=12×base×height

In the graph, the total area is 1 and the dotted area which is also called the density of the curve. Thus, the area of ΔACD or density of curve Y<1 can be calculated as:

Density of (Y<1)=12×base×height=12×1×1=0.5

Now, the probability of Y is less than 1 can be calculated as:

P(Y<1)=Density of Y<1Density of curve=0.51=0.5

Hence, the probability is 0.5.

Answer 20

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Answer 21

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Answer 22

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1. Construct a triangle on the left end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 2

Answer 23

Section 2:

Expert Solution

Answer 24

Section 2:

Expert Solution

Answer 25

Expert Solution

Answer 26

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

Answer 27

Section 3:

To determine

To find: The area.

Answer 28

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.5.

Answer 29

Section 3:

Expert Solution

Answer 30

Section 3:

Expert Solution

Answer 31

Expert Solution

Answer 32

Explanation of Solution

Calculation: From the provided triangle, base is equal to 1 and height is equal to 1. Thus, the area can be calculated as:

Area=12×base×height=12×1×1=0.5

Hence, the area is 0.5.

Answer 33

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Answer 34

(c)

Section 1:

To determine

To find: The probability P(Y>1.5).

Answer 35

(c)

Section 1:

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Answer 36

(c)

Section 1:

Expert Solution

Answer 37

(c)

Section 1:

Expert Solution

Answer 38

Expert Solution

Answer 39

Explanation of Solution

First, obtain the area in the interval of [0,1.5]. Thus, from the triangle

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 3

base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔBEF or the density of curve Y>1.5 can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 1.5 can be calculated as:

P(Y>1.5)=1−P(Y≤1.5)=1−Area of ΔBEFDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Answer 40

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Answer 41

Section 2:

To determine

To graph: The density curve and shade the area which represents the probability.

Answer 42

Section 2:

Expert Solution

Explanation of Solution

Graph: In the provided triangle, draw a vertical line at 1.5. Construct a triangle on the right end of the triangle and shade the left area. Hence, the density curve is shown below:

Introduction to the Practice of Statistics, Chapter 4.3, Problem 60E , additional homework tip 4

Answer 43

Section 2:

Expert Solution

Answer 44

Section 2:

Expert Solution

Answer 45

Expert Solution

Answer 46

Section 3:

To determine

To find: The area.

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

Answer 47

Section 3:

To determine

To find: The area.

Answer 48

Section 3:

Expert Solution

Answer to Problem 60E

Solution: The area is 0.125.

Answer 49

Section 3:

Expert Solution

Answer 50

Section 3:

Expert Solution

Answer 51

Expert Solution

Answer 52

Explanation of Solution

Calculation: From the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Hence, the area is 0.125.

Answer 53

(d)

To determine

To find: The probability P(Y>0.5).

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125

Now, the probability of Y is greater than 0.5 can be calculated as:

P(Y>0.5)=1−P(Y≤0.5)=1−Area of ΔAGHDensity of curve=1−0.1251=1−0.125

=0.875

Hence, the probability is 0.875.

Answer 54

(d)

To determine

To find: The probability P(Y>0.5).

Answer 55

(d)

Expert Solution

Answer to Problem 60E

Solution: The probability is 0.875.

Answer 56

(d)

Expert Solution

Answer 57

(d)

Expert Solution

Answer 58

Expert Solution

Answer 59

Explanation of Solution

Calculation: First, obtain the area in the interval of [0,0.5]. Thus, from the provided triangle, base is equal to 0.5 and height is equal to 0.5. Thus, the area can be calculated by the formula:

Area=12×base×height

The area of ΔAGH can be calculated as:

Area=12×base×height=12×0.5×0.5=0.125