The return on investment for a particular security has historically followed a normal distribution with a mean profit of 4.75% and standard deviation of 1.5%.If the historical pattern holds, what is the probability of investing in this security and seeing greater than a 6% return?
A) 0.7967
B) 0.8333
C) 0.2033
D) 0.1666

Question

Quizplus · Accepted Answer

We need to find the probability of getting a return greater than 6%. 
Using the formula for standardizing values in a normal distribution, we get:

z = (6 - 4.75) / 1.5 = 0.833

Looking up the area under the standard normal curve for this z-value using a table or calculator, we get:

P(Z > 0.833) = 1 - P(Z ≤ 0.833) = 1 - 0.7967 = 0.2033

Therefore, the probability of investing in this security and seeing a return greater than 6% is 0.2033 or 20.33%, which is option C.

The Return on Investment for a Particular Security Has Historically