# Probability Distributions

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Construct a probability distribution based on the following frequency distribution.

 Outcome 102 105 108 111 114 117 Frequency 10 20 45 15 20 15
1. Draw a graph of the hypothetical probability distribution.
2. Compute the expected value of the outcome.

ob Walters, who frequently invests in the stock market, carefully studies any potential investment. He is currently examining the possibility of investing in the Trinity Power Company. Through studying past performance, Walters has broken the potential results of the investment into five possible outcomes with accompanying probabilities. The outcomes are annual rates of return on a single share of stock that currently costs \$150. Find the expected value of the return for investing in a single share of Trinity Power.

 Return on investment (\$) 0 10 15 25 50 Frequency 0.2 0.25 0.3 0.15 0.1

f Walters purchases stock whenever the expected rate of return exceeds 10 percent, will he purchase the stock, according to these data?

Construct a probability distribution based on the following frequency distribution:

From the following graph of a probability distribution.

the only information available to you regarding the probability distribution of a set of outcomes is the following list of frequencies.

Bill Jonson has bought a VCR from Jim's Videotape Service at a cost of \$300. He now has the option of buying an extended service warranty offering 5 years of coverage for \$100. After talking to friends and reading reports, Bill believes the following maintenance expenses could be incurred during the next five years.

Steven T. Opsine, supervisor of traffic signals for the Fairfax Company division of the Virginia State Highway Administration, must decide whether to install a traffic light at the reportedly dangerous intersection of Dolley Madison Blvd. and Lewisville Rd. Toward this end, Mr. Opsine has collected data on accidents at the intersection.

S.H.A. policy is to install a trafic light at an intersection at which the monthly expected number of accidents is higher than 7. According to this criterion, should Mr. Opsine recommend that a traffic light be installed at this intersection?

Alan Sarkid is the president of the Dinsdale Insurance Company and he is concerned about the high cost of claims that take a long time to settle. Consequently, he has asked his chief actuary, Dr. Ivan Acke, to analyze the distribution of time until settlement. Dr. Acke has presented him with the following graph.