Ayoung investment manager tells his client that the probability of making a positive return with his suggested portfolio is 80%. if it is known that returns are normally distributed with a mean of 5.8%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation?

The risk, measured by standard deviation, that this investment manager assumes in his calculation is 0.0689

Step-by-step explanation:

Let X = rate of return

Since his client wants to make a positive return:

X > 0

P(X > 0) = 0.8

P(Z > (0-0.058)/sd) = 0.8

(0-0.058)/sd = -0.8416

-0.058/-0.8416 = standard deviation

standard deviation = 0.0689

Therefore, The risk, measured by standard deviation, that this investment manager assumes in his calculation is 0.0689

Option 2 - f(x)=-2

Step-by-step explanation:

Given : A line of best fit is f(x) ≈ −0.86x + 13.5 for the set of points in the table.

2    12

3    10

5    10

6     8

7     9

8     5

9     6

To find :  What is a good approximation for the value of the function, f(x), when x = 18?

Solution :

We have given the function,

The best fit for the value x=18, f(x) is

Approximately, For the value of x=18, f(x)=-2

Therefore, Option 2 is correct.