Step 1: The annual rate of return on stock indexes, which combine many individua

Question

Step 1:
The annual rate of return on stock indexes, which combine many individual stocks, is very roughly Normal. Since 1945, the Standard & Poor’s 500 index has had a mean yearly return of 12.5 percent with a standard deviation of 17.8 percent. Consider this Normal distribution to be the distribution of yearly returns over a long period.

In what range do the middle 95% of all yearly returns lie? ____% to _____%

I already know answer to step 1 is -231. to 48.1 - i just need help with step 2 and 3 thank you

Step 2: The market is down for the year if the return on the index is less than zero. The market is down in ___ proportion of years. (Give your answer to two decimal places and use a statistical table.)

Step 3: In what proportion of years does the index gain 25 percent or more? (Give your answer to two decimal places and use a statistical table to solve the problem.)

Step 1:
The annual rate of return on stock indexes, which combine many individual stocks, is very roughly Normal. Since 1945, the Standard & Poor’s 500 index has had a mean yearly return of 12.5 percent with a standard deviation of 17.8 percent. Consider this Normal distribution to be the distribution of yearly returns over a long period.

In what range do the middle 95% of all yearly returns lie? ____% to _____%

I already know answer to step 1 is -231. to 48.1 - i just need help with step 2 and 3 thank you

Step 2: The market is down for the year if the return on the index is less than zero. The market is down in ___ proportion of years. (Give your answer to two decimal places and use a statistical table.)

Step 3: In what proportion of years does the index gain 25 percent or more? (Give your answer to two decimal places and use a statistical table to solve the problem.)

Explanation / Answer

step 2: we know that mean is 12.5% or 0.125 and standard deviation is 17.8% or 0.178

We need P(x<0) or P(z<(0-0.125)/0.178)=P(z<-0.70) or 1-P(z<0.7), from normal distribution table this gives 1-0.758 or 0.242

step 3: P(x>0.25) or P(z>(0.25-0.125)/0.178)=P(z>0.7) or 1-P(z<0.7) which is 0.242step 2: we know that mean is 12.5% or 0.125 and standard deviation is 17.8% or 0.178

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