# The following table is a partial probability distribution for the MRA Company’s projected profits ( x = profit in $1000s) for the first year of operation (the negative value denotes a loss). x f ( x ) −100 .10 0 .20 50 .30 100 .25 150 .10 200 a. What is the proper value for f (200)? What is your interpretation of this value? b. What is the probability that MRA will be profitable? c. What is the probability that MRA will make at least$100,000?

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 5.2, Problem 14E
Textbook Problem
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## The following table is a partial probability distribution for the MRA Company’s projected profits (x = profit in $1000s) for the first year of operation (the negative value denotes a loss). x f (x) −100 .10 0 .20 50 .30 100 .25 150 .10 200 a. What is the proper value for f(200)? What is your interpretation of this value? b. What is the probability that MRA will be profitable? c. What is the probability that MRA will make at least$100,000?

Expert Solution

a.

To determine

Find the proper value for f(200) and to interpret the value.

### Explanation of Solution

Calculation:

The table represents the partial probability distribution for the MRA Company’s projected profits for the next year of operation.

The rules for a discrete probability distribution are,

• The sum of the probabilities must equal to 1. That is, f(x)=1.
• Each probability must be between 0 and 1, inclusive. That is, 0f(x)1.

Here, the sum of the probabilities is, 0

Expert Solution

b.

To determine

Find the probability that MRA will be profitable.

Expert Solution

c.

To determine

Find the probability that MRA will make at least \$100,000.

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