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.

A community playhouse needs to determine the​ lowest-cost production budget for an upcoming show. They have to determine which set pieces to construction and which to rent. The organization has only two weeks to construct the set. The theater has two carpenters who work up to 12 hours a​ week, each at ​$12 an hour.​ Additionally, the theater has a scenic artist who can work 15 hours per week to paint as needed at ​$14 per hour. The set needs 20 flats​ (walls), two hanging​ drops, and three wooden tables​ (props). The number of hours required for each piece for carpentry and painting is shown below.​ Flats, hanging​ drops, and props can also be rented at a cost of ​$75​, ​$500​, and ​$400 ​each, respectively. How many of each unit should be built by the theater and how many should be rented to minimize total​ cost?

The optimal integer solution is to build __ flat(s) and rent __ ​flat(s); build __hanging​ drop(s) and rent __hanging​ drop(s); build __prop(s) and rent__ prop(s). This solution gives the ▼(minimum, maximum) ​cost, which is ​$__.

FINANCIAL LEVERAGE EFFECTS

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $5.8 million with a 0.2 probability, $3 million with a 0.5 probability, and $0.8 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $17 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4 million with a 0.2 probability, $2.4 million with a 0.5 probability, and $0.8 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.