4. DETAILS MY NOTES ASK YOUR TEACHER Firehouse JJ has 3 engines with different capabilities and costs to run. If there is a fire call at position E28N31 then engine A gets to position E28N31 in a time, a, that is normally distributed with mean of 7 minutes and standard deviation 2 minutes, engine B gets to position E28N31 in a time b, that is normally distributed with mean of 12 minutes and standard deviation 4 minutes, and Engine C gets to position E28N31 in a time c, that is normally distributed with mean of 9 minutes and standard deviation 3 minutes. Engine A costs $300 per minute to operate, Engine B costs $200 per minute to operate and Engine C costs $400 per minute to operate. Let X = total engine operating time for Firehouse JJ engines on a call to position E28N31 and let W = total operating cost for Firehouse JJ engines on a call to position E28N31. More simply, X is defined as x = a + b + c. W = 300a + 200b + 400c. Note that a, b, and c are independent of one another. a) Calculate the expected value of X. [ b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) Calculate the standard deviation of W. | e) If we pick a value k such that the probability that X > k equals .25 then calculate k? f) What is the probability that the run to position E28N32 costs less than $10,000? [ g) What is the probability that X is within two standard deviations of its expected value? h) What is the probability that a is greater than c? [ i) What is the probability that a, b, and c are all less than their 75th percentiles? [