Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 32.6 and 4.9 mpg, respectively. [You may find it useful to reference the z table.] a. What is the probability that a randomly selected passenger car gets more than 36 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) b. What is the probability that the average mpg of two randomly selected passenger cars is more than 36 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) c. If two passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 36 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

12 cases of a disease are found over an area of 50 square miles.

(what type of distribution is this, i.e. Poisson, Gaussian, etc.)

1. Within the study area, if the cases are distributed at random places with the same chance to occur anywhere, what is the probability of finding 4 cases within an 8 square mile area? Calculate by hand.
2. What is the average number of cases within the 8 square mile area? Calculate by hand.

A transportation engineer is studying the distribution of fuel efficiencies (measured in miles per gal- lon, or mpg) for vehicles registered in Franklin county. Let Y denote the efficiency of a vehicle in mpg. The researcher models vehicle efficiency as following a normal distribution (i.e., the popula- tion distribution is normal) and randomly samples n = 16 vehicles from the population. The sample mean is y ̄ and the sample standard deviation is s. Answer the following questions. (If the exact values you need to solve these problems are not available in the appropriate table, use the closest values that are available.)

(a) Assume that the population mean of the efficiencies is μ = 30 but that the population stan- dard deviation is unknown. The calculated sample standard deviation is s = 5. What is the probability that the sample mean is within 2.5 mpg of the population mean?

(b) Estimate the mean efficiency in such a way that the accuracy is 1 mpg. Find the sample size (n) required to ensure that sample mean is within 1 mpg of the population mean with probability 0.90. Assume that the population standard deviation is known to be σ = 5.30.

(c) Assume that the population mean of efficiency is μ = 30 and the population standard deviation is known to be σ = 5.30. What is the probability that the sample standard deviation s is greater than 4?

5. Suppose that a car manufacturer claims that its fuel efficiency (as measured in miles per
gallon) per tankful of gasoline follows a normal distribution with mean 35 mpg and
standard deviation 2.0 mpg.
a) What percentage of tankfuls would obtain between 30 and 40 mpg? (A table of
standard normal probabilities appears at the end of this exam.)
b) Would the percentage of tankfuls that obtain between 30 and 40 mpg be larger,
smaller, or the same if the mean were larger than 35 (and the SD remained 2.0)? Explain your
answer.
c) Would the percentage of tankfuls that obtain between 30 and 40 mpg be larger, smaller,
or the same if the SD were larger than 2.0 (and the mean remained 35)? Explain your answer.

1. (No computer output is accepted) The mpg (miles per gallon) for all cars has a normal distribution with mean 100 km/L and standard deviation of 15 km/L.

a) Calculate the probability that any randomly selected car has an amount of mpg greater than 120 km/L.

b) Calculate the probability that any randomly selected car has an amount of mpg less than 95 km/L.

c) Calculate the probability that any randomly selected car has an amount of mpg between 93 km/L and 110 km/L.

d) A car is identified as a “best quality” if it is included in the top 2% of all mpgs. Find the minimum mpg needed to be qualified as “best quality”.

(Use 4 significant digits in your results. For example, if your answer is 20/7, write 2.8571. Moreover, do not leave the solution as 20/7. and , show your solutions in detail.)

Below is a frequency distribution for the estimated miles per gallon (MPG) for 530 different models of American-made cars.

(a) Identify the following

class midpoints (enter as a comma-separated list)

class boundaries (enter as a comma-separated list)

class width

(b) Create a relative frequency table from the frequency table.

(c) Create a cumulative and relative-cumulative frequency table.

(d) Estimate the mean MPG for the American-made cars included in this set.

1)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 38 months and a standard deviation of 10 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 48 and 68 months?

Do not enter the percent symbol.
ans = %

2)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 54 months and a standard deviation of 9 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 63 and 81 months?

Do not enter the percent symbol.
ans = %

Harris County is planning to construct a Dam some tens of miles away from the Houston Metropolis Recreation center to facilitate Power Generation and fishing in the El Santos River Basin. The first cost for the Dam will amount to $7,500,000. Annual maintenance and repairs will amount to $25,000 for the first six years, to $30,000 for each year in the next eight years, and to $35,000 per year for the next six years. At the end of the 20th year, $24,000 is estimated to be deposited into Harris county account as tax credits earned for its environmental compliance in the construction and operation of the Dam. In addition a major overhaul costing $550,000 will be required at the end of the seventh year. Use an interest rate of 10% and :

Determine the engineering economy symbols and their corresponding values.

Construct the cash flow diagram

Calculate the Capital Recovery for the project

Determine the total Annual Worth for the Project

What is the Present worth of this project

Consider this interactive scenario: The 1000 employees of the EconoPlant all live in QuietTown miles away. There are two roads from QuietTown to the EconoPlant, Wide Road and Narrow Road. Every day each employee needs to decide which road to take for commuting to work. The two roads differ in their commute time such that:

• Wide Road has a low-speed limit, but is sufficiently wide so that traffic does not cause a slowdown. The commute on Wide Road takes 40 minutes.

• Narrow Road has a higher speed limit, but congestion can slow traffic. The commute on Narrow Road takes 20 + m/10 minutes, where m is the number of drivers that take Narrow Road.

Employees aim to minimize commute time. Assume that people are identical in that each person chooses Narrow Road with a probability of p at equilibrium. So this is a symmetric mixed strategy equilibrium. Answer the following questions for a specific employee Colin:

(a) (1 point) What is Colin’s commute time on Wide Road?

(b) (1 point) Describe the number of Colin’s colleagues on Narrow Road at equilibrium as a function of p.

(c) (1 point) Suppose Colin chooses Narrow Road. Describe the total number of people on Narrow Road at equilibrium as a function of p.

(d) (1 point) Describe Colin’s commute time on Narrow Road at equilibrium as a function of p.

(e) (2 points) Without solving for p, what is the numerical value of Colin’s equilibrium commute time on Narrow Road that you get in part (d)? Briefly explain how you get the numerical value.

(f) (2 points) What is the equilibrium strategy of each employee? (In other words, what is the value of p at equilibrium?)

The table below contains the overall miles per gallon​ (MPG) of a type of vehicle. Complete parts a and b below.

a. Construct a 99% confidence interval estimate for the population mean MPG for this type of​ vehicle, assuming a normal distribution. The 99​% confidence interval estimate is from:

MPG to MPG.

​(Round to one decimal place as​ needed.)

b. Interpret the interval constructed in​ (a)