A stock broker has compiled a list of 100 (risky) stocks that are forecasted to

Question

A stock broker has compiled a list of 100 (risky) stocks that are forecasted to outperform the market an average of 6% during the coming year (independent of other stocks). In the fine print, we read that this outperformance percentage for each stock is actually a random variable with a Ar(6.15) distribution. We plan to invest $10,000 according to one of the following strategies: 1. Select 4 of the stocks and invest equally in each. 2. Select 16 of the stocks and invest equally in each. 3. Select 36 of the stocks and invest equally in each. Note that the outperfonnance percentage of each investment is X. For each strategy: a Find the sampling distribution of X. b. Find P{X > 10), i.e.. our investment outperforms the market by at least 10%. c. Find P(X erforms the market. 3.1.15. Find the smallest positive integer a for which 1001 x + 770>

Explanation / Answer

a) it will be a simple sampling distribution of x bar as the stocks are normally distributed.

b) mean = 6

variance = 15

threfore standard deviation = sqrt(15) = 3.87

p(x>10) =

For x = 10, z = (10 - 6) / 3.87 = 1.03

Hence P(x > 10) = P(z > 1.03) = [total area] - [area to the left of 1.03]

= 1 - 0.8485 = 0.1515

c) p(x<0) =

For x = 0, the z-value z = (0 - 6) / 3.87 = -1.55

Hence P(x < 0) = P(z < -1.55) = [area to the left of -1.55] = 0.0606

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