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a.
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.
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.
The calculation of the expected value (Z) for the outcome being equal to or lower than $31,200 is shown below.
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.
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.
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.
The calculation of the expected value (Z) for the outcome being equal to or lower than $33,600 is shown below.
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.
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.
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.
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.
d.
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.
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.
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.
e.
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.
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.
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.
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.
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Chapter 13 Solutions
Foundations of Financial Management
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