Question

You may need to use the appropriate appendix table to answer this question. The average return for large-cap domestic stock funds over three years was 14.4%. 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 17%? (Round your answer to four decimal places.) (b) What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? (Round your answer to four decimal places.) (c) How big does the return have to be to put a domestic stock fund in the top 15% for the three-year period? (Round your answer to two decimal places.)

Answer 1

x~inliy,4 yoy) al Pl x311) - 1-P12 312144 2 -C :-1- P1282.51 =1012779| bl pl x & lo) - plz & 10-14.4) 44. =plz I -1.) = 0.1587 S : : P(x) 0. 3 Plx<*)__30:15 3) -14.4 4.4 as Scanne wick CamScanner 1 9,84]

Answer 2

SOLUTION :

Average return = mean = 14.4%

SD = 4.4% 

a.

P(x ≥ 17%) 

= P(z ≥ (17 - 14.4) / 4.4 )

= P(z ≥ 0.59)

= 1 - P(z < 0.59)

= 1 - 0.7224. (from cumulative ND table)

= 0.2776 (ANSWER).

b.

P( x ≤ 10%) 

= P(z ≤ (10-14.4)/4.4)

= P(z ≤ - 1.0)

= 0.1587 (ANSWER)

c.

Top 15% = Right tail of ND = 0.15 

Let it be at a z value of standard ND.

So, below this z-score, probability = 1 - 0.15 = 0.85.

From Nd table,

z = 1.03 + 0.01(8500 - 8485)(8508-8485)

=> z = 1.03652 

=> x = z*SD + mean

=> x = 1.03652 * 4.4 + 14.4

=> 18.96% 

Return should be ≥ 18.96% to be in top 15% funds. (ANSWER).