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

a) the probability is .01 that the sample standard deviation is bigger than what number?

b) the probability is .025 that the sample standard deviation is smaller than what number?

c) find any pair of numbers such that the probbility that the sample standard deviation lies between these numbers is .90.

a medicine company produces pills containing an active ingredient. the company is concerned about the mean weight of this ingredient per pill, but it also requires that the variance be no more than 1.5. a random sample of 20 pills is selected, and the sample variance is found to be 2.05. how likely is it that a sample variance this high or higher would be found if the population variance is in fact 1.5? assume that the population distribution is normal.

thanks.