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. Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software or statistical table.

Referring to Table 6-6, find the probability that the annual return of a random year will be less than 11.5%.

Referring to Table 6-6, find the probability that the annual return of a random year will be more than 11.5%.

Referring to Table 6-6, find the probability that the annual return of a random year will be between 7.5% and 11%.

Referring to Table 6-6, find the probability that the annual return of a random year will be less than 7.5%.

Referring to Table 6-6, find the probability that the annual return of a random year will be more than 7.5%.

Referring to Table 6-6, what is the value above which will account for the highest 25% of the possible annual returns?

Referring to Table 6-6, 75% of the annual returns will be lower than what value?

Referring to Table 6-6, find the two values that will bound the middle 50% of the annual returns.

Referring to Table 6-6, find the two values that will bound the middle 80% of the annual returns.

Referring to Table 6-6, 10% of the annual returns will be less than what amount?

Referring to Table 6-6, 10% of the annual returns will be at least what amount?