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The following data collected from the Australian Bureau of Meteorology Website (http://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data (includes all forms of precipitation such as rain, drizzle and hail) for the year 2018 in Tully, Queensland (Station number 32042). The zero values indicate no rainfall and the left-most column gives the date. Assuming that the weekly rainfall event (number of days in a week with rainfall) follows a Poisson distribution (There are 52 weeks in a year and a week is assumed to start from Monday.):
(i) What is the probability that on any given week in a year there would be no rainfall?
(ii) What is the probability that there will be 3 or more days of rainfall in a week?
(b) Assuming that the weekly total amount of rainfall (in mm) from the data provided in part (a) has a normal distribution, compute the mean and standard deviation of weekly totals.
(i) What is the probability that in a given week there will be between 10mm and 50mm of rainfall?
(ii) What is the amount of rainfall if only 12% of the weeks have that amount of rainfall or higher?
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