Question

Annual returns on stock of the Mean Corporation are approximately normally distributed with a mean of 13.9% and standard deviation of 4.9%. Joe Prudent is considering investing in the Mean Corporation. According to his investment strategy, he will only invest if the chance of an annual return of 11% or more is greater than 70%. In answering the following question, a)Calculate the corresponding standardized value (z) for an annual return of 11%. Give your answer to 2 decimal places. z = b)Therefore, according to his investment strategy, Joe: will invest in Mean Corporation will not invest in Mean Corporation is indifferent to investing in Mean Corporation

Answer 1

Answer:

(a) z=-0.59

(b) Joe will invest in Mean Corporation. The probability of getting an annual return grater than 11% is 72.3%.

Step-by-step explanation:

We have a normal distribution for the annual return of the stock.

This distribution has mean of 13.9% and s.d. of 4.9%.

If X=11%, we can calculate its corresponding z-value as:

$z=\frac{X-\mu}{\sigma}= \frac{0.11-0.139}{0.049}= -0.5918$

The z-value is z=-0.5918.

The probabilty of P(X>11%)=P(y>-0.5918) is, by the standarized normal distribution table, equal to 0.723.

As its P(y>-0.5918)=P(X>11%)=0.723 bigger than the 70% threshold, Joe will invest in Mean Corporation.