Question

An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 12.2% and standard deviation 7.2%.

A. For what proportion of these corporations was the rate of return higher than 20%?
B. For what proportion of these corporations the rate of return negative?
C. For what proportion of these corporation was the rate of return between 5% and 15%?

Answer 1

To find the proportions of corporations with different rates of return, we can use the normal distribution and calculate the z-scores.

Step-by-step explanation:

To find the proportion of corporations with a rate of return higher than 20%, we need to calculate the z-score for 20% and then find the corresponding area under the normal curve. The z-score can be calculated using the formula:

z = (x - μ) / σ

where x is the value we want to find the proportion for (20% in this case), μ is the mean (12.2%), and σ is the standard deviation (7.2%). The area under the normal curve can then be found using a standard normal distribution table or a calculator.

For the proportion of corporations with a negative rate of return, the z-score would be:

z = (0 - μ) / σ

Using the same process as above, we can find the area under the normal curve.

To find the proportion of corporations with a rate of return between 5% and 15%, we need to find the area under the normal curve between the z-scores for 5% and 15%. This can be done using the cumulative distribution function (CDF) of the normal distribution.