# statistics: probability question

• Mar 24th 2011, 01:32 PM
dan0408
statistics: probability question
A company is interested in investing in companies in Hong Kong. They have access to a large data set on the rate of return on assets (expressed as a percentage) for a large number of companies operating in Hong Kong and have noticed that the data are normally distributed with mean = 9 and Standard deviation = 21

Explain how the company could use the information above to assess the probability of a company having a rate of return above or below a given figure. (Thinking)
• Mar 24th 2011, 02:02 PM
dwsmith
Quote:

Originally Posted by dan0408
A company is interested in investing in companies in Hong Kong. They have access to a large data set on the rate of return on assets (expressed as a percentage) for a large number of companies operating in Hong Kong and have noticed that the data are normally distributed with mean = 9 and Standard deviation = 21

Explain how the company could use the information above to assess the probability of a company having a rate of return above or below a given figure. (Thinking)

$\displaystyle \cdots -3\sigma-\mu=-54, \ -2\sigma-\mu=-33, \ -\sigma-\mu=-12, \ \mu=9, \ \sigma+\mu=30, \ 2\sigma+\mu=51, \ 3\sigma+\mu=72\cdots$

Since it is normal distributed, what percent falls between $\displaystyle \pm\sigma, \ \pm 2\sigma, \ \pm 3\sigma\text{?}$
• Mar 24th 2011, 02:02 PM
pickslides
Do you know the (68-95-99.7)% rule?
• Mar 25th 2011, 12:31 AM
dan0408
nope i do not know that rule
• Mar 27th 2011, 12:44 PM
pickslides
Its the answer to the question in post #2. Can you link the ideas?
• Mar 27th 2011, 02:15 PM
HallsofIvy
More generally, if the desired rate of return is x, calculate the "standard variable" $\displaystyle z= \frac{x- 9}{21}$ and look up the probability in a table of the standard normal distribution. A good one is at Standard Normal Table.