The USGS has maintained a stream gage on Big Creek at Hill City since 1964. The highest discharge recorded at this gage was 45,000 cfs in 1972. The base-10 logs of the annual peak discharges in cfs for WY 1965-2013 have a mean of 3.678 and a standard deviation of 0.456. Assume that the probability distribution of the annual peak discharges is log-normal (the logs of the annual peak discharges are normally distributed). Note: the recurrence interval of a discharge is the reciprocal of its annual exceedance probability.
1.) Find the discharge with an annual exceedance probability of 0.02.
2.) Find the annual exceedance probability of the 1972 flood.