Answer:
a) 68% of the investments had a return of between 10% and 30%.
b) 32% of investments had a return that was either less than 10% or morethan 30%.
Explanation:
We can use the Empirical Rule to solve this question:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean. This also means that 32% of the measures are more than 1 standard deviation from the mean.
95% of the measures are within 2 standard deviation of the mean. This also means that 5% of the measures are more than 2 standard deviations from the mean.
99.7% of the measures are within 3 standard deviations of the mean. This also means that 0.3% of the measures are more than 3 standard deviations from the mean.
In this problem, we have that:
Mean = 20%.
Standard deviation = 10%.
a. What proportion of the investments had a return of between 10% and 30%?
10 is the mean subtracted by 1 one standard deviation
30 is one standard deviation added to the mean.
So 10 and 30 are within 1 standard deviation of the mean. So 68% of the investments had a return of between 10% and 30%.
b. What proportion of investments had a return that was either less than 10% or morethan 30%?
This is the proportion of investments that were farther than one standard deviation of the mean.
By the Empirical Rule, 32% of investments had a return that was either less than 10% or morethan 30%.