Reference no: EM132850911

The annual rate of return on stock indexes (which combine man individual stocks) is approximately normal. Since 1945, the Standard & Poor's 500 Index has had a mean yearly return of 13%, with a standard deviation of 19.5%. Take this normal distribution to be the distribution of yearly returns over a long period.

(a) In what range do the middle 95% of all yearly returns lie?

(b) The market is down for the year if the return on the index is less than -1.24%. In what proportion of years is the market down?

(c) In what proportion of years does the index gain 28.41% or more?