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A government is convinced that to properly control the inflation of the country, all it needs to do is to ensure that the annual rate of ination is between 3% and 6%. The reserve bank in the country has informed the government that the annual force of ination It. recorded in each month I, can be modelled with the following equation I, = 0.81,-1 + 0.012, where Z; ~ N(1.1). The current annual rate of ination is 6%. a] Assume that the rate of ination is lognormally distributed, nd the distribution of I12 , the rate of ination in month 12. b] Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is between 3% and 6%. c} Assuming that the government and the reserve bank are correct in their assertions, calculate the probability that the annual rate of inflation is less than 3%