A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%.The probability of getting a return between -28% and 64% in any one year is
A) 68.26%
B) 95.44%
C) 99.74%
D) 100.00%

Question

Quizplus · Accepted Answer

Given: 
Expected Return (μ) = 18%
Standard Deviation (σ) = 23%
We need to find the probability of getting a return between -28% and 64% in any one year.
For this, we need to convert the returns into standard units of deviation using the formula:
z = (x - μ)/σ
Where x is the return we are interested in and z is the corresponding z-score.

So, for a return of -28%:
z1 = (-28% - 18%)/23% = -1.74

And for a return of 64%:
z2 = (64% - 18%)/23% = 2.43

Now, we can use a standard normal distribution table (or calculator) to find the probability of getting a return between z1 and z2.
The probability of getting a z-score between -1.74 and 2.43 is approximately 0.9544 or 95.44%.
Therefore, the answer is B.

A Security with Normally Distributed Returns Has an Annual Expected