Task 4. A thrifty engineering student is concerned about not exceeding her budget for gasoline, so she conducts a Monte Carlo simulation to see what range of costs her driving might incur. The cost can be determined from miles driven, fuel economy in miles per gallon (MPG), and cost per gallon for fuel. Her budget is $700 for the year. The inputs to the cost are all normally distributed mean and standard deviation given in the form (mean, SD): mileage (6000, 1000); miles per gallon (30, 4); cost of fuel ($3.25, $0.25). a. What is the expected value for her spending for the year? Does she expect to stay within budget? b. Now suppose she runs the simulation, and for a single replicate or iterate, generates the following random numbers between O and 1, as the basis for calculating a value: for miles driven, 0.139; for fuel economy, 0.355; for the cost of fuel, 0.437. What is the annual cost returned for this replicate? Is the value within budget? c. Carry out a Monte Carlo simulation of the problem generating 1000 replicates and provide the average value of the sample, a histogram of the probability of being in appropriate cost bins, and the percent of iterates that are above the $700 threshold