TABLE 6-6 According to Investment Digest, the Arithmetic Mean of the Annual

question 182

Short Answer

TABLE 6-6
According to Investment Digest, the arithmetic mean of the annual return for common stocks from 1926-2010 was 9.5% but the value of the variance was not mentioned. Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric. Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software or statistical table.
-Referring to Table 6-6, find the probability that the annual return of a random year will be more than 7.5%.

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Definitions:

Random Cause Variation

Variability in data or processes that is caused by numerous uncontrollable factors, observed in a natural, random spread of results.

Centerline

In the context of statistical process control charts, this is the median line around which the plotted values are expected to vary.

Random Variation

The natural fluctuation in data or process outcomes, occurring without a specific, predictable cause.

Sample Proportion

The ratio of the number of times an event occurs to the total number of observations or trials in the sample.