Solve with correct answers

STAT10118 52 (b) Patrick and Hemi plan to compete against each other in a 100-metre sprint. Based on previous results they know that Patrick's race times are normally distributed with a mean of 11.5 seconds and a variance of 1.5 seconds. Hemi's race times are normally distributed with a mean of 10.5 seconds and a variance of 2.5 seconds. Let P be the random variable for the time it takes Patrick to complete the race and H be the random variable for the time it takes Hemi. Assume the times are independent. (i) What is the expected value of the random variable D, where D = P - H, the difference in Patrick and Hemi's race times? (ii) Show that the standard deviation of D is 2 seconds. (il) Sketch the distribution for D, clearly labelling the important features on your sketch (iv) Describe in a sentence how to find the probability that in a randomly chosen race Herris faster than Patrick, using your answers from parts (1) to (ul) above You do NOT need to work this outUse the results from parts (A) and (B) to estimate the average profit per grill if 41 grills are produced. (C) Estimated average profit = (1 point) Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) = 5200 + 9x + 0.01x2 + 0.0002x3. (a) Find the marginal cost function. Answer:where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 6000 dollars with an additional cost of 200 dollars per unit. (A) Find the revenue function in terms of x. R(x) = (B) Use the financial department's estimates to determine the cost function in terms of X. C(x) = (C) Find the profit function in terms of .. P(x) = (D) Evaluate the marginal profit at x = 250. P' (250) =Evaluate the marginal revenue at the following values: (A) R' (400) = (B) R' (650) = (1 point) The total profit (in dollars) from the sale of x espresso machines is P(x) = 50x - 0.6x2 - 230