Question

Exit Submit Assignment for Glduiry ions Exercise 06.18 (Self-Test) Algorithmic Question 3 of 3 Check My Work (2 remaining) O Video The average return for large-cap domestic stock funds over t hree years 2009-2011 was 14.5%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.9%. Use Table 1 in Appendix B. a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)? b. What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)? C. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period (to 2 decimals)? Check My Work (2 remaining) Question 3 of 3 O-Icon Key Exercise 06.18 (Self-Test) Algorithmic Email Instructor Save Exit Submit Assignment for Grading Cengage Learning Cengage Technical Support

Answer 1

a)

Here, μ = 14.5, σ = 4.9 and x = 20. We need to compute P(X >= 20). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (20 - 14.5)/4.9 = 1.12

Therefore,
P(X >= 20) = P(z <= (20 - 14.5)/4.9)
= P(z >= 1.12)
= 1 - 0.8686 = 0.1314

b)

Here, μ = 14.5, σ = 4.9 and x = 10. We need to compute P(X <= 10). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (10 - 14.5)/4.9 = -0.92

Therefore,
P(X <= 10) = P(z <= (10 - 14.5)/4.9)
= P(z <= -0.92)
= 0.1788

c)

z value at 10% = 1.28

z =(x - mean)/sigma
1.28 = (x - 14.5)/4.9
x = 4.9 * 1.28 + 14.5
x =20.77