Two team (A and B) play a series of baseball games. The team who wins three games of five-game-series wins the series. Consider A has home-field advantage (0.7 means A has probability of winning 0.7 if it plays in its field) and opponent-field disadvantage (0.2 means A has probability of winning 0.2 if it plays in opponents field). If the series start on A team’s field and played alternately between A and B team’s fields, find the probability that series will be completed in four games.

1f. Compare 1a and 1d, and 1b and 1e, explain why the percentage in 1a is much larger than that in 1d and why the value in 1b is much smaller than that in 1e?

1. Suppose that for Edwardsville High School, distances between students’ homes and the high school observe normal distribution with the average distance being 4.76 miles and the standard deviation being 1.74 miles. Express distances and z scores to two decimal places. Write the formula to be used before each calculation.

1a. What percentage of students in the high school live farther than 6.78 miles from the school?

1b. A survey shows that 8% of the students who live closest to the school choose to walk to school. What is the maximum walking distance of these 8% of students? In other words, what is the distance below which these 8% of students live from the school?

1c. Suppose that the school district’s policy allows students living beyond 4.50 miles from the school to take school buses to go to school. There are 3,567 students who enroll in the fall semester, 2006. How many students in the high school are not eligible to take school buses?

1d. Suppose all samples of size 12 are taken. What percentage of sample means has a value larger than 6.78 miles?

1e. Below what value are 8% of sample means of size 12?

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer calculating miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at fill-up. The driver wants to determine if these calculations are different.

(b) Carry out the test. (Round your answer for t to four decimal places.)
t =?

(c) Give the degrees of freedom.

(d) Give the P-value. (Round your answer to four decimal places.)

Using JAVA:

This assignment is about aggregation and class collaboration.

You will create several Classes that will be part of an overall class named InstrumentDisplay. The classes are FuelGage, Odometer, MilesSinceLastGas, and CruisingRange.

The FuelGage should assume a 15 gallon tank of gasoline and an average consumption of 1 gallon every 28 miles. It should increment in 1 gallon steps when you "add gas to the tank". It should decrement by 1 every 28 miles. It should display its current value.

You should also have a display that shows how many miles traveled since you last added gasoline, MilesSinceLastGas, and a display for the estimated number of miles until you run out of gasoline, the CruisingRange.

The Odometer should keep track of total mileage from 0 to 999,999. After that it turns over back to 0. Make sure your code allows for this rollover.

The overall class is to be named InstrumentDisplay. You may create the various outputs using System.out or JOptionPane. Make sure that account for both filling and emptying the tank. While your odometer will display in 1 mile increments, you should keep track of mileage internally in one tenth of a mile increments for purposes of computing gasoline remaining in the FuelGage and miles in the CruisingRange

Please make sure you comment your code thoroughly.

The code should be nicely formatted and should use proper variables.

A road perpendicular to a highway leads to a farmhouse located 22 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph.55mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 11 miles past the intersection of the highway and the road?

The distance between the automobile and the farmhouse is increasing at a rate of  miles per hour.

A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM. How fast the trains are separating after long time?

In 10 test runs, a truck operated for 8, 10, 10, 7, 9, 12, 10, 8, 7, and 9 miles with one gallon of a certain gasoline. Is this evidence at the 0.05 level of signifcance that the truck is not operating at an average of 11.5 miles per gallon with this gasoline? What assumptions must be satised in order for the procedure you used to analyze these data to be valid?

A truck acquired at a cost of $260,000 has an estimated residual value of $12,550, has an estimated useful life of 49,000 miles, and was driven 3,900 miles during the year. Determine the following. If required, round your answer for the depreciation rate to two decimal places.

Why are satellites normally sent into orbit by firing them in an easterly direction? Based on this, explain why the International Space Station (ISS) orbits the Earth at about 17,500 miles per hour at an altitude above Earth’s surface of about 230 miles. Would it be more efficient to have a higher or lower orbit for the ISS? Explain in detail why or why not.