According to Investment Digest (\"Diversification and the Risk/Reward Relationsh

Question

According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 16.5%, and the standard deviation of the annual return was 19%.

In later parts of the question we will ask:

a. What is the probability that the stock returns are greater than 0%?
b. What is the probability that the stock returns are less than 18%?

For this part, answer the following question:

What is the value of the test statistic (Z, t, or F) for each part? (Round to 2 decimal digits)

Question 2 options:

-0.87 in part a, -0.06 in part b

-0.67 in part a, 0.06 in part b

-0.87 in part a, 0.08 in part b

0.67 in part a, 0.08 in part b

**This was all information provided**

-0.87 in part a, -0.06 in part b

-0.67 in part a, 0.06 in part b

-0.87 in part a, 0.08 in part b

0.67 in part a, 0.08 in part b

**This was all information provided**

Explanation / Answer

Answer in details with calculations and explanation below:

Params of normal distribution have been given :

Mean = 16.5%
Stdev = 19%

We normalize using the above params:

a. P(X>0) = P(Z> 0-16.5/19) = P(Z>-16.5/19) = .81

b. P(X<18) = P(Z< 18-16.5/19) = P(Z< 1.5/19) = .53

c. We have used Z statistic in each part as Z statistic represents converting distribution into normal distribution

2) In 1st part -16.5/19 is -0.87 and 2nd part 1.5/19 = 0.08. So, right answer is C

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