Suppose you have the choice between two investments - one that pays fixed interest of 4% p.a. ,and another whose returns are normally distributed with an expected return of 10% and standard deviation of 3%.What is the likelihood of receiving a return on the second investment that is equal to or greater than that which can be received from the first investment? (Hint: the area under a curve for 1 std dev is 34.13%,2 std dev is 47.73% and 3 std dev is 49.87%. )
A)97.73%
B)84.13%
C)65.87%
D)52.27%

Question

Quizplus · Accepted Answer

To find the likelihood of receiving a return on the second investment that is equal to or greater than 4%, we calculate how many standard deviations 4% is from the mean (10%). The difference is 10% - 4% = 6%. Since the standard deviation is 3%, 6% is 2 standard deviations below the mean. The area under the curve to the right of -2 standard deviations (which represents higher returns) is 50% (half of the curve) plus the area from -1 to 0 standard deviations (34.13%) plus the area from 0 to -2 standard deviations (47.73%). However, since we're looking at the area to the right of -2 standard deviations, we consider the entire area under the curve except for the leftmost 2.27% (100% - 97.73%). Thus, the likelihood of receiving a return equal to or greater than 4% is 97.73%.

Suppose You Have the Choice Between Two Investments - One