Question

If the daily returns on the stock market are normally distributed with a mean of .05% and a standard deviation of 1%, the probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately __________.A. .0%B. .1%C. 1%D. 10%

Answer 1

A. .0%

Step-by-step explanation:

A normally distributed means 99% of the cases are contain within 3 standard deviation up or down fro mthe median in this case; the range between:

0.005 - 0.01 x 3 //0.005+0.01*3 = -0.025//0.025 = -2.5%//2.5%

-2.5%//2.5% between these values is 99% of the cases.

The 23% is so far away that his probabilities are enarly zero.

We can also calcualte this by normalize the asked return and look the z value on a nrmal distribution table:

(X-median)/standard deviaiton = z

(-0.23 -0.005)/0.01 = -23.5

P(z<23.5) = As it isn't n the table, the chances are zero because are inginificant low.