Suppose that the returns on an investment are normally distributed with an expected return of 16% and standard deviation of 3%.What is the likelihood of receiving a return that is equal to or less than 19%? (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)15.87%
D)2.27%

Question

Quizplus · Accepted Answer

To find the likelihood of receiving a return that is equal to or less than 19%, we need to find the area under the normal curve up to 19%. First, we need to standardize the 19% return using the formula: z = (x - μ) / σ, where x is the return, μ is the expected return, and σ is the standard deviation. Thus, z = (19 - 16) / 3 = 1. To find the area under the normal curve up to z = 1, we can look up the corresponding value in the normal distribution table or use a calculator. The area is approximately 0.8413 or 84.13%. Therefore, the likelihood of receiving a return that is equal to or less than 19% is 84.13%. The best choice is B.

Suppose That the Returns on an Investment Are Normally Distributed