A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 70 thousand miles and a standard deviation of 12 thousand miles. Complete parts​ (a) through​ (c) below.

a. What proportion of trucks can be expected to travel between 53 and 70 thousand miles in a​ year? (Round to four decimal places as​ needed.)

Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 29 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives at least 42 miles in a day. Round your answer to four decimal places.

Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 33 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives at least 169 miles in a day. Round your answer to four decimal places.

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 120 miles from the point and has a speed of 480 miles per hour. The other is 160 miles from the point and has a speed of 640 miles per hour.

(a)At what rate is the distance between the planes changing? In MPH

(b)How much time does the controller have to get one of the airplanes on a different flight path? in MIN

A manufacturer of a certain type of tires claims that their tire lifetime is 30,000 miles. The Bureau of Consumer Protection wants to conduct an preliminary investigation on this claim.

a. If the true lifetime is only 29,000 miles, what is the chance that the Bureau won’t be able to detect such difference with data only on 16 tires? Assume that the SD of all tire lifetimes is about 1,500 miles.

b. How many tires should the Bureau test on so that they can detect the lifetime of 29,000 miles or less with 90% power?

miles of frequent travelers (miles) / # employees

Danube recently acquired a delivery van for $24,200 paying cash. Danube projects a 4 year useful service life and a remaining residual value on the delivery van of $2,200. Danube expects to drive the van 106,000 miles during the useful service life. Please compute the annual depreciation for the 4 year life of the delivery van for each of these methods:

1. Straight-line

Depreciation expense

2. Double-declining-balance. (Round your depreciation rate to 2 decimal places. Round your final answers to the nearest whole dollar.) End year ammounts. Years 1,2,3, with depreciation expense, accumulated depreciation and book value for each year.

3. Actual miles driven each year were 19,000 miles in Year 1; 29,000 miles in Year 2; 23,000 miles in Year 3; and 25,000 miles in Year 4. Note that actual total miles of 96,000 fall short of expectations by 10,000 miles. Calculate annual depreciation for the four-year life of the van using activity-based. (Round your depreciation rate to 2 decimal places.) end of year amounts year 1, 2, 3, 4, with depreciation expense, accumulated depreciation and book value for each year.

Please explain via excel with formulas

8b What is the probability that at least four of ten new customers would Enroll in the new Program (using all the data)? Exactly seven? Less than six? Now compute these same questions and report your findings based on the new probability value after you remove the customers that were given No Offer. Briefly explain how the results change.

In Taiwan, no one goes to work, and everyone consumes a single good (food), which is imported from another place and can be purchased (one meal at a time) from the nearest vending machine. Alternatively, food can be delivered by a distant catapult, capable of flinging a meal through a customer's window. The price of a delivered catapult meal is $8 and the price of a vending-machine meal is $2. The travel cost for consumers is $1 per roundtrip mile ($0.5 per mile traveled).

a. How many miles would the market area (i.e. maximum miles to be traveled for vending) for the vending machine be?

b. Show your answer in a martini shaped glass, indicating the slope of the glass’ arms, price of food at vending machine, and the radius of the city. (Label your axes)

c. Now assume that everyone owns a bike, which reduces the travel cost to $0.2 per round-trip mile. What would the new market area be for the vending machine?

d. Continue from part c above (everyone owns a bike still). Assume that a new vending machine replaces the old one, now allowing customers to purchase 2 meals at a time (meals are storable at no cost). How would that affect (if any) the market area of the vending machine?

e. Continue from part d above, and assume that everyone eats 2 meals per day in this town, and a month is 30 days long. What would the monthly rent difference be for a residence located 5 miles v. 10 miles away from the vending machine? (Hint: a single daily trip to the vending machine is sufficient).