The average stock price for companies making up the SP 500 i

The average stock price for companies making up the S&P 500 is $26.00 and the standard deviation is unknown. Assume the stock prices are normally distributed.

If 26% of the stock prices are more than $45.75, what is the variance? (Remember the label.)

Solution

P(X>45.75)=0.26

--> P((X-mean)/s <(45.75-26)/s) =1-0.26=0.74

--> P(Z<19.75/s) =0.74

--> 19.75/s = 0.64 (from standard normal table)

So s = 19.75/0.64 =30.85938

So variance= 30.85938^2 =952.3013