The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 25 and a standard deviation of 2. The population distribution can be assumed as normal. A random sample of these cars is taken.

a. Find the probability that the sample mean fuel consumption will be fewer than 24 miles per gallon if (i) a sample of 1 observation is taken, (ii) a sample of 4 observations if taken and (iii) a sample of 16 observations is taken.

b. Explain why the three answers in part a. differ in the way they do. Draw a graph to illustrate your reasoning.

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Ho: m < 26 Ha: m > 26 Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25

At 99% confidence, what is the critical value?

Test to determine whether or not the tire company is using legitimate advertising. hypothesis

On January 1, Year 1, the City Taxi Company purchased a new taxi cab for $90,000. The cab has an expected salvage value of $38,000. The company estimates that the cab will be driven 200,000 miles over its life. It uses the units-of-production method to determine depreciation expense. The cab was driven 45,000 miles the first year and 102,000 the second year. What would be the depreciation expense reported on the Year 2 income statement and the book value of the taxi, respectively, at the end of Year 2?

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine. ​(a) Compute the​ z-score corresponding to the individual who obtained 38.4 miles per gallon. Interpret this result. ​(b) Determine the quartiles. ​(c) Compute and interpret the interquartile​ range, IQR. ​(d) Determine the lower and upper fences. Are there any​ outliers? 32.5; 35.9; 37.6; 38.6; 40.4; 42.5; 34.0; 36.2; 37.8; 38.9; 40.6; 42.6; 34.7; 37.3; 38.1; 39.4 ;41.3; 43.4; 35.6; 37.4; 38.4; 39.7; 41.8; 49.1

A six-lane freeway (three lanes in each direction) operates at capacity during peak hour. It has 11-ft

lanes, 4-ft right shoulders, and there are three ramps within three miles upstream of the segment

midpoint and four ramps within three miles downstream of the segment midpoint. The freeway has an

AADT of 60,000 veh/day. The traffic stream has 8% heavy vehicles, and it is on rolling terrain with a

peak- hour factor of 0.85. It is known that 12% of the AADT occurs in the peak hour and that the

directional factor is 0.6. What is the freeway’s LOS?

3. A small fire is sighted from ranger stations A and B. The bearing of the fire from station A is N35E, and the bearing of the fire from station B is N49W. Station A is 1.3 miles due west of station B.

a) How far is the fire from each station?

b) At fire station C, which is 1.5 miles from A, there is a helicopter that can be used to drop water on the fire. If the bearing of C from A is S42E, find the distance from C to the fire, and find the bearing of the fire from

C. Note: A neat labeled diagram is required.

On January 1, 2018, the Excel Delivery Company purchased a delivery van for $57,000. At the end of its five-year service life, it is estimated that the van will be worth $5,400. During the five-year period, the company expects to drive the van 172,000 miles.

Required:
Calculate annual depreciation for the five-year life of the van using each of the following methods.

1. Straight line.
2. Sum-of-the-years’-digits.
3. Double-declining balance.
4. Units of production using miles driven as a measure of output, and the following actual mileage:

Depreciation Methods

A delivery truck costing $19,000 is expected to have a $1,500 salvage value at the end of its useful life of four years or 125,000 miles. Assume that the truck was purchased on January 2. Calculate the depreciation expense for the second year using each of the following depreciation methods: (a) straight-line, (b) double-declining balance, and (c) units-of-production. (Assume that the truck was driven 28,000 miles in the second year.) Round all answers to the nearest dollar.

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine.

32.4
34.1
34.5
35.7
36.1
36.3
37.5
37.7
37.9
38.1
38.3
38.5
38.7
39.1
39.5
39.8
39.9
40.6
41.3
41.6
42.3
42.7
43.8
49.0