According to Investment Digest, the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5%, but the value of the variance was not mentioned. Also 25% of the annual returns were below 8%, while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric. Answer the following questions without the help of a calculator, statistical software or statistical table.

a.find the probability that the annual return of a random year will be between 7.5% and 11%.

b. what is the value above which will account for the highest 25% of the possible annual returns?

c.75% of the annual returns will be lower than what value?

d.find the two values that will bound the middle 50% of the annual returns.

e.find the two values that will bound the middle 80% of the annual returns.

f.10% of the annual returns will be less than what amount?