An investment strategy has an expected return of 7 percent and a standard deviat

Question

An investment strategy has an expected return of 7 percent and a standard deviation of 4 percent. Assume investment returns are bell shaped. a. How likely is it to earn a return between 3 percent and 11 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.) Probability b. How likely is it to earn a return greater than 11 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.) Probability c. How likely is it to earn a return below 1 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.) Probability

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standatd deviation)

Mean = 7 percent

Standard deviation = 4 percent

A)Probability that the return is between 3 and 11 percent = P(3 < X < 11) = P(X < 11) - P(X < 3)

3 and 11 are one standard deviation from the mean 7 (7+4 = 11 and 7-4 = 3)

So, according to 68, 95, 99.7 rule, the probability of the events that lies within one standard deviation from mean = 0.68

B) Probability that return will be greater than 11 percent = P(x > 11)

= 1 - P(x < 11)

= 1 - P(z < (11-7)/4)

= 1 - P(z < 1)

= 1 - 0.84 = 0.16

C) Probability of return less than -1 percent = P(x < - 1) = P(z < (-1 - 7)/4)

= P(z < - 2)

= 0.02

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