APRA, the Australian Prudential Regulatio Authority, monitors the return rates of large superannuation funds in Australia. Its publication Statistics: Quarterly superannuation performance, December 2016 showed an annual rate of return of 6.8% for the year. 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 7.5% with a standard deviation of 0.7% and that rates of return were normally distributed.

a. If researcher selects an individual fund at random from this population, what is the probability that the fund had a return of:

i. less than 8.2%

ii. between 6.9% and 7.8%

iii. greater than 7.9%

b. If random sample of 10 funds is selected from this population, what is the probability that the sample mean lies in the ranges given in (a)?