IAn investment strategy has an expected return of 9 percent and a standard deviation of 5 percent. Assume investment returns are bell shaped.

Question

a. How likely is it to earn a return between 4 percent and 14 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.)



b. How likely is it to earn a return greater than 14 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.)


c. How likely is it to earn a return below −1 percent? (Enter your response as decimal values (not percentages) rounded to 3 decimal places.)

Answer 1

a. To find the likelihood of earning a return between 4 percent and 14 percent, we need to find the area under the bell curve between these two points. This can be calculated using the standard normal distribution.

First, we need to convert the values of 4 percent and 14 percent to standard deviations from the mean. The formula for this is:
Z = (X - μ) / σ

Where Z is the number of standard deviations from the mean, X is the value we want to convert, μ is the mean (expected return), and σ is the standard deviation.

For 4 percent:
Z1 = (4 - 9) / 5 = -1

For 14 percent:
Z2 = (14 - 9) / 5 = 1

Next, we need to find the area under the standard normal distribution curve between Z1 and Z2. We can use a standard normal distribution table, or a calculator with a built-in function for this.

For Z1 = -1, the area under the curve to the left of Z1 is 0.1587.
For Z2 = 1, the area under the curve to the left of Z2 is 0.8413.

Therefore, the area between Z1 and Z2 is: 0.8413 - 0.1587 = 0.6826.

So, the likelihood of earning a return between 4 percent and 14 percent is 0.6826, or 68.26%.

b. To find the likelihood of earning a return greater than 14 percent, we need to find the area under the curve to the right of Z2.

Using the standard normal distribution table, the area to the left of Z2 is 0.8413.

Therefore, the area to the right of Z2 is 1 - 0.8413 = 0.1587.

So, the likelihood of earning a return greater than 14 percent is 0.1587, or 15.87%.

c. To find the likelihood of earning a return below -1 percent, we need to find the area under the curve to the left of Z1.

Using the standard normal distribution table, the area to the left of Z1 is 0.1587.

So, the likelihood of earning a return below -1 percent is 0.1587, or 15.87%.