APRA, the Australian Prudential Regulation Authority, monitors the return rates of

large superannuation funds in Australia. Imagine that a researcher with access to the

APRA data finds that the average rate of return for the largest superannuation funds

in the last year has been 8.5% with a standard deviation of 0.7% and that rates of

return were normally distributed.

a. If the researcher selects an individual fund at random from this population, what

is the probability that the fund had a return of:

i. less than 9.5%?

ii. between 7.9% and 8.3%?

iii. greater than 8.8%?

b. If a random sample of 10 funds was selected for this population, what is the

chance that the sample mean would lie in the ranges given in (a)?