A hospital analyzed the relationship between the distance an employee must travel between home and work (in 10s of miles) and the annual number of unauthorized work absences (in days) for several randomly selected hospital employees. The regression analysis showed df_Err = 15, SS_xx = 23.88, SS_yy = 130.00, and SS_xy = -54.50.

What is the 99% confidence interval for β₁ (with appropriate units)?

Suppose that the speed at which cars go on the freeway is normally distributed with mean 74 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If one car is randomly chosen, find the probability that it is traveling more than 73 mph.

c. If one of the cars is randomly chosen, find the probability that it is traveling between 77 and 80 mph.

d. 78% of all cars travel at least how fast on the freeway? mph.

You plan to purchase a car for $28,000. Its market value will decrease by 20% per year. You have determined that the IRS-allowed mileage reimbursement rate for business travel is about right for fuel and maintenance at $0.485 per mile in the 1st year. You anticipate that it will go up at a rate of 10% each year, with the price of oil rising, influencing gasoline, oils, greases, tires, and so on. You normally drive 15,000 miles per year. Your MARR is 9%.

What is the optimum replacement interval for the car?

Show the EUAC value used to reach your decision: $

2. A world class runner can run long distances at a pace of 15 km/hour. That runner expends 800 kilocalories of energy per hour.

a. Find the power (in Watts [W]) the runner is exerting while running. (3 points

b) Find the total energy (in Joules [J]) exerted by the runner in a 15 km run.

c. How many Milky Way (Original Single 52.2g) chocolate bars does the runner need to buy to supply the amount of energy to complete a half-marathon (13.1 miles)? (Cite your source for the number of calories in a Milky Way bar)

You plan to purchase a car for $28,000. Its market value will decrease by 20% per year. You have determined that the IRS-allowed mileage reimbursement rate for business travel is about right for fuel and maintenance at $0.485 per mile in the 1st year. You anticipate that it will go up at a rate of 10% each year, with the price of oil rising, influencing gasoline, oils, greases, tires, and so on. You normally drive 15,000 miles per year. Your MARR is 9%.

What is the optimum replacement interval? Show the EUAC value you used to reach your decision.

Please find if there are any outliers in this data set using the Z-score. This must be done in excel so please show the formulas used!

Suppose that the speed at which cars go on the freeway is normally distributed with mean 65 mph and standard deviation 7 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If one car is randomly chosen, find the probability that it is traveling more than 66 mph.

c. If one of the cars is randomly chosen, find the probability that it is traveling between 68 and 72 mph.

d. 63% of all cars travel at least how fast on the freeway?  mph.

3.    Last year the Rainforest Conservation Society (a Canadian environmental group) purchased the commercial hunting rights to an area of 7,700 square miles in British Columbia. The group’s plan is to ban hunting in this area. While this type of bargaining has been recognized for years as a potential solution to protect wildlife, why has it not been implemented very often?

4. Certain environmental laws prohibit EPA from considering the costs of meeting various standards when the levels of the standards are set. Is this a good example of “putting first things first” or simply an unjustifiable waste of resources? Why?