An investment strategy has an expected return of 14 percent and a standard devia
ID: 3159015 • Letter: A
Question
An investment strategy has an expected return of 14 percent and a standard deviation of 9 percent. Assume investment returns are bell shaped. a. How likely is it to earn a return between 5 percent and 23 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 23 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 4 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.) Probability
Explanation / Answer
A)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 5
x2 = upper bound = 23
u = mean = 14
s = standard deviation = 9
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1
z2 = upper z score = (x2 - u) / s = 1
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.158655254
P(z < z2) = 0.841344746
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.682689492 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 23
u = mean = 14
s = standard deviation = 9
Thus,
z = (x - u) / s = 1
Thus, using a table/technology, the right tailed area of this is
P(z > 1 ) = 0.158655254 [ANSWER]
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c)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = -4
u = mean = 14
s = standard deviation = 9
Thus,
z = (x - u) / s = -2
Thus, using a table/technology, the left tailed area of this is
P(z < -2 ) = 0.022750132 [ANSWER]
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