Da Best coffee roasters claim that the actual weight of a 200 gram (g) packet of their coffee beans can be modelled as a continuous random variable, X, with the probability density function: fx(x) = [0.04r-7.86 for 199 < < 204 otherwise (a) Find the probability that a randomly chosen 200g packet of Da Best coffee beans will: be underweight (ie, contain less than 200g of coffee beans) be overweight (ie, contain more than 200g of coffee beans) contain exactly 200g of coffee beans. (b) How much do we expect Da Best 200g packets of coffee beans to weigh on average? Quote your answer to 4 decimal places. (e) Calculate E(X). Quote your answer to 2 decimal places. (d) The median weight m of 200g packets of Da Best coffee beans can be found by solving the equation: 0.02m -7.86m+771.62 = 0. The solutions to the equation 0.02m -7.86m + 771.62 = 0 are m = 190.9 and m=202.1 (1 decimal place). Use this information to state, with a justification, the median weight of 200g packets of Da Best coffee beans. Calculate P(X2 m), where m is the median weight of 200g packets of Da Best coffee beans. (e) Da Best coffee roasters charge $7 for a 200g packet of their coffee beans. Manufacturing and labour are costed at $4 per packet and the coffee beans cost them 1 cent per gram. Let P be the profit in dollars on one packet of coffee beans. Calculate E(P), the expected profit on one packet of coffee beans. Quote your answer to 4 decimal places. Var (X) Calculate the ratio Var(P) without computing Var(X) and Var(P).