Final answer:
To find the proportion of corporations with negative rate of return, we can use the properties of the normal distribution. Using the mean and standard deviation provided, calculate the z-score for a rate of return of 0%. Then, use a z-score table or calculator to find the proportion of values below the calculated z-score.
Step-by-step explanation:
To find the proportion of corporations in the investment portfolio whose rate of return was negative, we can use the properties of the normal distribution. Given that the rates of return follow a normal distribution with a mean of 9.5% and a standard deviation of 6.2%, we can calculate the z-score for a rate of return of 0% (negative return). Using the z-score table or a calculator, we can find the proportion of values below the calculated z-score, which represents the proportion of corporations with a negative rate of return.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
where z is the z-score, x is the value of interest (0% in this case), μ is the mean (9.5%), and σ is the standard deviation (6.2%).
Substituting the values, we get:
z = (0 - 9.5) / 6.2
z = -1.5323
Using a z-score table or a calculator, we find that the proportion of values below a z-score of -1.5323 is approximately 0.0639. Therefore, approximately 6.39% of the corporations in the investment portfolio had a negative rate of return.