Each member of a random sample of 15 business economists was asked to predict the rate of inflation for the coming year. Assume that predictions for the whole population of business economists follow a normal distribution with standard deviation 1.8%.

a. The probability is 0.01 that the sample standard deviation is bigger than what number?

b. The probability is 0.025 that the sample standard deviation is smaller than what number?

c. Find a pair of numbers (say a and b) such that the probability that the sample standard deviation lies between these two numbers is 0.90.