Using the data below, what percentage of data would you predict would be between 25 and 50 and what percentage would you predict would be more than 50 miles? Then determine the percentage of data points in the dataset that fall within each of these ranges. How do each of these compare with your prediction and why is there a difference?

Predicted percentage between 25 and 50 miles:

Actual percentage between 25 and 50 miles:

Predicted percentage of more than 50 miles:

The actual percentage of more than 50 miles:

Comparison:

Why?:

Drive

36

20

88

6

71

42

76

63

36

63

38

28

55

33

40

80

86

83

4

39

25

25

54

54

81

73

29

76

78

77

42

36

71

94

6

An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon.

Car   Weight (pounds), x   Miles per Gallon, y
A   2695   26.7
B   2975   23.6
C   3260   24.9
D   3760   23.1
E   4225   20.4

a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

Write the equation for the​ least-squares regression line.

Modifying Above y with carety =__x+__

(b) Interpret the slope and​ intercept, if appropriate.

(c) Predict the miles per gallon of car B and compute the residual. Is the miles per gallon of this car above average or below average for cars of this​ weight?

D) Draw the​ least-squares regression line on the scatter diagram of the data and label the residual.

(All answers were generated using 1,000 trials and native Excel functionality.)

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

Would a person traveling at a constant 500 miles an hour feel a greater amount of force than a person traveling at a constant 50 miles an hour? Why or why not?

The epicenter of an earthquake is the point on Earth's surface directly above the earthquakes origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Find the location of the earthquake's epicenter if it is 3 miles away from A(2,3), 4 miles away from B(-5,3), and 5 miles away from C(-1,-2).

The EPA sticker for a particular model of automobile claims the car has average highway mileage of 35 miles per gallon. A consumer advocacy group takes a random sample of 30 of these cars and finds that they have an average mileage of 33.6 miles per gallon with a standard deviation of 3 miles per gallon. Do the results of this test provide sufficient evidence to conclude that the actual mileage of this model is less than 35 miles per gallon? Translate this into a statistical hypothesis and carry out the test of hypothesis. Be sure to specify the null and alternative hypotheses, the value of the test statistic, the p-value, and your conclusion.

A company purchases a salesman a car for $40,000; the salesman pays $2,000 for an upgraded sound system to make his time on the road more pleasant. The car has an expected salvage value of $2,000 and an expected life of 4 years or 200,000 miles.

During the first year the car was driven 45,000 miles, during the second year 40,000 miles and 50,000 miles the 3rd year

Please show the annual depreciation expense for years 1, 2, 3 using straight line depreciation, double declining balance method, and units of production method. For each method, show the car's book value at the end of year 3.

You are required to show your work on each problem on this exam. The following rules apply:

• Clearly and neatly present and show your work for each problem.

• Mysterious or unsupported answers will not receive full credit. A correct answer, unsupported by calculations, explanation, or other work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations might still receive partial credit.

MARIGINAL AND JOINT DISTRIBUTIONS

The joint distribution of X and Y is as follows.

a. Find the marginal distribution of X and Y.

b. Find the conditional distribution of X given y = 1

c. Compute the conditional expectation of Y given X=1, E{Y=y|X=1}