18. The average return for large-cap domestic stock funds over the three years 2

Question

18. The average return for large-cap domestic stock funds over the three years 2009-2011 was 14.4% (AAII Journal, February 2012). Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4% a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20%? b. What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? c. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period? Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S News & World Report website, January 5, 2015). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Answer the following ques- tions about the cost of automobile repairs. a. What is the probability that the cost will be more than $450? b. What is the probability that the cost will be less than $250? c. What is the probability that the cost will be between $250 and $450? d. If the cost for your car repair is in the lower 5% of automobile repair charges, what 19. is your cost?

Explanation / Answer

Pls, one Question at a time.

19.

Normal distribution params are given :

Mean = 367
SD = 88
a. P(X>450) = P(Z>(450-367)/88) = P(Z>.943) = .1738
b. P(X<250) = P(Z<-1.33) = .0918
c. P(250<X<450) = P(X<450)-P(X<250) = .1738-.0918 = .0820
d. P(X<=c) = .05, Z is -1.645, So , (c-367)/88) = 1.645, So, c = 88*-1.645 +367 = 222.24

So, cost for lower 5% is $222.24

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