Please show work The expected return of a mutual fund is 8%. If the standard dev
ID: 2741019 • Letter: P
Question
Please show work
The expected return of a mutual fund is 8%. If the standard deviation of the mutual fund is 2.5%, what are the chances the return of the fund will be less than 13%?
Assume a normal distribution. A. 32% B. 68% C. 84% D. 95% E. 97.5%
The expected return of a mutual fund is 8%. If the standard deviation of the mutual fund is 2.5%, what are the chances the return of the fund will be less than 5.5%?
Assume a normal distribution. A. 2.5% B. 16% C. 32% D. 68% E. 95%
The expected return of a mutual fund is 8%. If the standard deviation of the mutual fund is 2.5%, what is the minimum return you would expect 84% of the time? Assume a normal distribution.
A. 5.5% B. 10.5% C. 13% D. 16% E. 3%
Explanation / Answer
1)Calculation of the probability of the return of the fund will be less than 13%
expected return of a mutual fund =8%
standared devaition of mutual fund = 2.5%
first we calculate the Z score
Standardizing a random variable X is done by subtracting X from the mean value (), and then dividing the result by the standard deviation (). The result is a standard normal random variable which is denoted by the letter Z.
so z= (X- )/
=(13-8)/2.5
=+2.00
Next, one would often consult a Z-table for cumulative probabilities for a standard normal distribution in order to determine the probability. In this case, for Z = +2.00
= 97.725, or 97.5%.
so answer is E
2)
1)Calculation of the probability of the return of the fund will be less than 5.5%
expected return of a mutual fund =5.5%
standared devaition of mutual fund = 2.5%
first we calculate the Z score
Standardizing a random variable X is done by subtracting X from the mean value (), and then dividing the result by the standard deviation (). The result is a standard normal random variable which is denoted by the letter Z.
so z= (X- )/
=(5.5-8)/2.5
=-1.00
Next, one would often consult a Z-table for cumulative probabilities for a standard normal distribution in order to determine the probability. In this case, for Z = -1.00
= 15.866, or 16%.
so answer is B
c)Calculation of the expected retuen of the probability is 84%
first we found out the z score in Z-table for cumulative probabilities for a standard normal distribution in order to determine the probabilityis =84%
so z score is =+1
z= (X- )/
+1 =(X-8)/2.5
2.5 =X-8
X = 10.5%
minimum return is 10.5
so answer is B