(a) The following data collected from the Australian Bureau of Meteorology Website (http://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall...
Question:
(a) 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 for the year 2014 in Sydney (recorded in mm at Sydney Airport). The zero values indicate no rainfall and the left-most column gives the date. Assuming that Rainfall or No-Rainfall event follows a Poisson distribution:
(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 2 or more days of rainfall in a week? (There are 52 weeks in a year and a week is assumed to start from Monday).
(b) Assuming that the weekly total amount of rainfall 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 4 mm and 12 mm of rainfall?
(ii) What is the amount of rainfall if only 8% of the weeks have that amount of rainfall or higher?