Foundations Of Financial Management
Foundations Of Financial Management
17th Edition
ISBN: 9781260013917
Author: BLOCK, Stanley B., HIRT, Geoffrey A., Danielsen, Bartley R.
Publisher: Mcgraw-hill Education,
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Chapter 13, Problem 20P

a.

Summary Introduction

To calculate: The probability that the outcome will be between $16,800 and $31,200.

Introduction:

Probability:

The likelihood of the occurrence of an event or of a proposition to be true, when expressed numerically or quantitatively, is termed as probability.

a.

Expert Solution
Check Mark

Answer to Problem 20P

The probability that the outcome will be between $16,800 and $31,200 is 0.8664.

Explanation of Solution

The calculation of the expected value (Z) for the outcome being equal to or greater than $16,800 is shown below.

Z=Lower RangeExpected Value (X)Standard Deviation (σ)=$16,800$24,000$4,800=$7,200$4,800=1.5

The calculation of the expected value (Z) for the outcome being equal to or lower than $31,200 is shown below.

Z=Upper RangeExpected Value (X)Standard Deviation (σ)=$31,200$24,000$4,800=$7,200$4,800=1.5

The Z values are positive as well as negative 1.5. Hence, the probability of the outcome being between $16,800 and $31,200 is 0.8664.

b.

Summary Introduction

To calculate: The probability that the outcome will be between $14,400 and $33,600.

Introduction:

Probability:

The likelihood of the occurrence of an event or of a proposition to be true, when expressed numerically or quantitatively, is termed as probability.

b.

Expert Solution
Check Mark

Answer to Problem 20P

The probability that the outcome will be between $14,400 and $33,600 is 0.9544.

Explanation of Solution

The calculation of the expected value (Z) for the outcome being equal to or greater than $14,400 is shown below.

Z=Lower RangeExpected Value (X)Standard Deviation (σ)=$14,400$24,000$4,800=$9,600$4,800=2

The calculation of the expected value (Z) for the outcome being equal to or lower than $33,600 is shown below.

Z=Upper RangeExpected Value (X)Standard Deviation (σ)=$33,600$24,000$4,800=$9,600$4,800=2

The Z values are positive as well as negative 2. Hence, the probability of the outcome being between $14,400 and $33,600 is 0.9544.

c.

Summary Introduction

To calculate: The probability that the outcome will be at least $14,400.

Introduction:

Probability:

The likelihood of the occurrence of an event or of a proposition to be true, when expressed numerically or quantitatively, is termed as probability.

c.

Expert Solution
Check Mark

Answer to Problem 20P

The probability that the outcome will be at least $14,400 is 0.9544.

Explanation of Solution

The calculation of the expected value (Z) for the outcome being at least $14,400 is shown below.

Z=Lower RangeExpected Value (X)Standard Deviation (σ)=$14,400$24,000$4,800=$9,600$4,800=2

The expected value is 0.4772 when Z is (+ or -) 2 and 0.5000 when Z is 0. So, the probability of the outcome being at least $14,400 is 0.9772. The graph of this probability is shown below.

Foundations Of Financial Management, Chapter 13, Problem 20P , additional homework tip  1

d.

Summary Introduction

To calculate: The probability that the outcome will be less than $31,900.

Introduction:

Probability:

The likelihood of the occurrence of an event or of a proposition to be true, when expressed numerically or quantitatively, is termed as probability.

d.

Expert Solution
Check Mark

Answer to Problem 20P

The probability that the outcome will be less than $31,900 is 0.9544.

Explanation of Solution

The calculation of the expected value (Z) for the outcome being at least $14,400 is shown below.

Z=Upper RangeExpected Value (X)Standard Deviation (σ)=$31,900$24,000$4,800=$7,900$4,800=1.65

The expected value is 0.4505 when Z is (+ or -) 1.65 and 0.5000 when Z is 0. So, the probability of the outcome being at least $14,400 is 0.9505. The graph of this probability is shown below.

Foundations Of Financial Management, Chapter 13, Problem 20P , additional homework tip  2

e.

Summary Introduction

To calculate: The probability that the outcome will be less than $19,200 or greater than $26,400.

Introduction:

Probability:

The likelihood of the occurrence of an event or of a proposition to be true, when expressed numerically or quantitatively, is termed as probability.

e.

Expert Solution
Check Mark

Answer to Problem 20P

The probability that the outcome will be less than $19,200 or greater than $26,400 is 0.4672.

Explanation of Solution

The calculation of the expected value (Z) for the outcome being less than $19,200 is shown below.

Z=Lower RangeExpected Value (X)Standard Deviation (σ)=$19,200$24,000$4,800=$4,800$4,800=1

The expected value is 0.3413 when Z is (+ or -) 1 and 0.5000 when Z is 0. So, the probability of the outcome being less than $19,200 is 0.1587 (0.5000 – 0.3413).

The calculation of the expected value (Z) for the outcome being greater than $26,400 is shown below.

Z=Upper RangeExpected Value (X)Standard Deviation (σ)=$26,400$24,000$4,800=$2,400$4,800=0.5

The expected value is 0.1915 when Z is (+ or -) 1 and 0.5000 when Z is 0. So, the probability of the outcome being at least $14,400 is 0.3085 (0.5000 – 0.1915).

Hence, the probability that the outcome will be less than $19,200 or greater than $26,400 is 0.4672. The graph of this probability is shown below.

Foundations Of Financial Management, Chapter 13, Problem 20P , additional homework tip  3

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