Answer Happy

"SonicBoom" records distribute CDs and LPs to retail outlets around North America. They distribute packages to three different outlets in Toronto, A, B and C say, the weights of the packages sent to each being independent and Normally distributed but with different means and standard deviations. The means and standard deviations are given (in kg) in the table below: Outlet A Outlet B Outlet C Mean Standard Deviation 3.50 5.50 7.60 0.30 0.30 1.30 Part a) To cut costs, SonicBoom sometimes aggregates together packages for the three Toronto outlets for shipping. Assume a parcel is sent that comprises of one package for each outlet. Write down the probability distribution for the weight of the parcel. Find the probability (to two decimal places) that the total weight of the parcel will exceed 15 kg but be less than 16 kg. Part b) One month, SonicBoom sends two packages to outlet A, three packages to outlet B, and one to outlet C. Write down the probability distribution for the total weight of the packages posted that month. Find the probability (to two decimal places) that the total weight is greater than 33.00 kg. Part c) Find the probability (to two decimal places) that the weight of a package to outlet C will be at least double the weight of a package to outlet A.