# Probability Distributions For Continuous Variables

A large company is planning to launch a new product in the market. However, the company is not sure about the state of the economy and its impact on the return on the capital investment associated with this new product. A key analysis in this regard is the expected return and risk. Since the new product can come in three different versions, each associated with a different capital investment, the company formed three teams each involved in an independent project to determine which project generates the highest expected return. The analysis in each project made in the context of the chance of economical change is shower in the table.

Sate of the Economy

Probability of Occurrence Project

1 Project

3 Project

2

Downward (Recession) 0.6 4 6 7

No Change (Stable) 0.3 5 7 8

Upward (Booming) 0.1 12 14 16

a. Determine each project's expected return and variability in return

b. Which project yields the highest expected return and low risk

Given the probability distributions of Stock A and Stock B illustrated in the Table, calculate:

a. The expected return for each stock

b. The variability in return associated with each stock

Probability Stock A Stock B

0.4 5 4

0.25 10 11

0.15 12 14

0.1 13 15

0.1 13 16

The weekly gross income of a local restaurant assistant manager follows a normal probability distribution with a mean of 1000 and a standard deviation of 100.

a. What are the z values for the income of assistant managers earning between 900 and 1100 weekly? What is the percent of assistant managers earning this range of income?

b. What are the z values for the income of assistant managers earning between 800 and 1200 weekly? What is the percent of assistant managers earning this range of income?

c. What are the z values for the income of assistant managers earning between 700 and 1100 weekly? What is the percent of assistant managers earning this range of income?

d. What are the z values for the income of assistant managers earning less than 860 weekly? What is the percent of assistant managers earning this range of income?

e. What are the z values for the income of assistant managers earning more than 1050 weekly? What is the percent of assistant managers earning this range of income?

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#### Solution Preview

See the attached file.

State of the Economy Probability of Occurrence Project 1 Project 3 Project 2

Downward (Recession) 0.6 4 6 7

No Change (Stable) 0.3 5 7 8

Upward (Booming) 0.1 12 14 16

a. Determine each project's expected return and variability in return

For project 1,

Expected ...

#### Solution Summary

The solution determines the probability distributions for continuous variables.