1 The average return for largecap domestic stock funds over

1. The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.7%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.8%.

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)?

2. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015 (BusinessWeek, March 20, 2006). Assume the standard deviation is $3,380 and that debt amounts are normally distributed.

a. What is the probability that the debt for a randomly selected borrower with good credit is more than $18,000 (to 4 decimals)?

b. What is the probability that the debt for a randomly selected borrower with good credit is less than $10,000 (to 4 decimals)?

c. What is the probability that the debt for a randomly selected borrower with good credit is between $12,000 and $18,000 (to 4 decimals)?

d. What is the probability that the debt for a randomly selected borrower with good credit is no more than $14,000 (to 4 decimals)?

Solution

average return for large-cap domestic stock funds - X is N(14.7, 4.8)

a) P(atleast 20)

= P(X>20)

= P(Z>1.104)

= 0.1357

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b) P(X<10) = P(Z<-0.98)

= 0.1635

c) P(X<c) = 0.90

z >1.285

X >20.85

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2) X - the mean debt for revolving and installment accounts is N(15015, 3380)

a) P(X>18000) = P(Z>0.88)

=0.1894

b) P(X<10000) = P(Z<=-1.48)

=0.0694

c) P(12000<x<18000)

= P(-.89<Z<0.88) = 0.6239

d) P(X<14000)

= 0.3821