Suppose that 26 of 200 tires of brand A failed to last 30,000 miles whereas the corresponding figures for 200 tires of brands B, C, and D were 23, 15, and 32. Test the null hypothesis that the failure rates of the four tire brands are 10% at the 0.05 level of significance.

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 141 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Let X = the average of the 49 races. Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) X ~ , Part (b) Find the probability that the runner will average between 138 and 142 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min Part (d) Find the median of the average running times. min

Based on annual driving of 15,000 miles and fuel efficiency of 20 mpg, a car in the United States uses, on average, 700 gallons of gasoline per year. If annual automobile fuel usage is normally distributed, and if 26.76% of cars in the United States use less than 480 gallons of gasoline per year, what is the standard deviation?

Round your answer to 2 decimal places, the tolerance is +/-0.05.

The data provided give the gasoline mileage​ (in miles per​ gallon) based on the horsepower of a​ car's engine and the weight of the car​ (in pounds). Using the data​ provided, determine the VIF for each independent variable in the model. Is there reason to suspect the existence of​ collinearity?

Determine the VIF for each independent variable in the model.

Round to three decimal places as​ needed.

5.1 A car is traveling along a highway at 65 miles per hour. The road is horizontal (0% slope). If the wind resistance and rolling resistance at the wheels creates a combined resistive force of 950 N, what is the power (kW) developed at the rear wheels?

5.2 How much power (kW) must the car engine in problem 5.1 develop if the overall mechanical efficiency of the transmission and drive train is 94%?

5.3 Assume the car engine in problem 5.1 is operated on gasoline with an energy content of 113,500 Btu's per gallon, and that the thermal efficiency of the spark ignition engine and drivetrain is 28.6%. What is the fuel efficiency of the car in miles per gallon?

5.4 The car in problem 5.1 approaches a mountain and begins ascending a grade of 6.0%. If the car maintains an uphill speed of 70 miles per hour, how much additional power (kW) must be developed by the engine to overcome the change in elevation? Assume the car has a mass of 1400 kg.

5.5 Assume the car above is operated on a blend of 85% ethanol and 15% gasoline (E85). If the energy content of ethanol is 80,460 Btu's per gallon, what is the energy content of the E85 fuel (Btu/gal)?

5.6 Assume the overall thermal efficiency of the engine and drivetrain of the car above drops to 24.5% when operated on E85 fuel. What is the estimated fuel economy (km/L) of the car above when subjected to the uphill operating conditions above (Problem 5.4)?

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 37 months and a standard deviation of 4 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 25 and 29 months? Do not enter the percent symbol. ans =

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 149 minutes with a standard deviation of 12 minutes. Consider 49 of the races.
Let X = the average of the 49 races.

a.) X ~ N (149, ? )

b.Find the probability that the runner will average between 148 and 151 minutes in these 49 marathons. (Round your answer to four decimal places.)

c. Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)

d. Find the median of the average running times.

A sample of 20 Automobiles was taken and the miles per gallon (MPG), horsepower (HP), and total weight were recorded. Develop a linear regression model to predict MPG…

1)Using HP as the independent variable. What is the regression equation?

2) Is your model a good predicting equation? How do you know?

3) Using Total Weight as the independent variable, what is the regression equation?

4)Is this a good predicting model? How do you know?

5) Using MPG and Total weight as independent variables, what is the regression equation?

6) Is the model in part e a good predicting equation? How do you know?   

7)  Predict MPG using the model in part e with HP = 100 and weight = 3 thousand pounds.

According to the U.S. Federal Highway Administration, the mean number of miles driven annually is 12,200 with a standard deviation of 3800 miles. A resident of the state of Montana believes the drivers in Montana drive more than the national average. She obtains a random sample of 35 drivers from a list of registered drivers in the state and finds the mean number of miles driven annually for these drivers to be 12,895.90. Is there sufficient evidence to show that residents of the state of Montana drive more than the national average?

What is the p-value for this hypothesis test?
What is the test statistic for this hypothesis test?
What is the critical value?
What is the decision?

Options: