1.            The completion times for the government exam used for entrance into Officer Candidate School is uniformly distributed between 85 minutes and 145 minutes.

                A.            What is the probability someone finishes the exam between 95 and 120 minutes?

                B.            What is the probability it takes a candidate at least 110 minutes to finish the exam?

Make sure you round to 4 decimal places where appropriate.

2.            The average daily commuting distance for a San Diegan is 31 miles with a standard deviation of 5.8 miles. If commuting distances are normally distributed:

                A.            What is the probability that a person commutes at most 35 miles?

                B.            What is the probability that a person commute is between 25 and 38 miles?

C.            What would someone have to commute to be in the top 6% of longest commutes (Where does the Top 6% start)?

Make sure you round to 4 decimal places where appropriate.

When you answer the question put the 5 answers in this order and label like this:

1A.

1B.

2A.

2B.

2C.

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 256 brakes using Compound 1 yields an average brake life of 49,386 miles. A sample of 298 brakes using Compound 2 yields an average brake life of 47,480 miles. Assume that the population standard deviation for Compound 1 is 1649 miles, while the population standard deviation for Compound 2 is 3911 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

Step 1 of 3 : Find the point estimate for the true difference between the population means.

Step 2 of 3: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to sox decimal places.

Step 3 of 3: Construct the 80% confidence interval. Round your answers to the nearest whole number.

9. As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. By following the six-step procedure for hypothesis testing found below, answer the following: At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees?

Step 1: State the Null Hypothesis (H_0) and the Alternate Hypothesis (H_1)

Step 2: Determine the level of significance. (Note: It’s given in this problem!)

Step 3: Select the Test Statistic

Step 4: Formulate the Decision Rule

Step 5: Make a Decision

Step 6: Interpret the Result

A property and casualty insurance company (which provides fire coverage for dwellings) felt that the mean distance from a home to the nearest fire department in rural Alabama was at least 10 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 10 miles due to the increased number of volunteer fire departments. This, they felt, would convince the insurance company to lower its rates. They randomly identify 64 homes and measure the distance to the nearest fire department for each. The resulting sample mean was 8.7 miles. If σ = 3.5 miles, does the sample show sufficient evidence to support the community’s claim? Use the four step process for Hypothesis Testing.

Step 1 – State Hypothesis in context of the problem.

Step 2 – Gather data, check assumptions, and find rejection region using α.

Step 3 – Calculate the appropriate test statistic and p-value.

Step 4 – State conclusion in context of the problem.

Find the maximum value and minimum value in milesTracker. Assign the maximum value to maxMiles, and the minimum value to minMiles. Sample output for the given program:

Min miles: -10
Max miles: 40

Java Code: Remember we can only add to the code. We cant change whats already given. Thank you.

import java.util.Scanner;

public class ArraysKeyValue {
public static void main (String [] args) {
Scanner scnr = new Scanner(System.in);
final int NUM_ROWS = 2;
final int NUM_COLS = 2;
int [][] milesTracker = new int[NUM_ROWS][NUM_COLS];
int i;
int j;
int maxMiles; // Assign with first element in milesTracker before loop
int minMiles; // Assign with first element in milesTracker before loop

for (i = 0; i < milesTracker.length; i++){
for (j = 0; j < milesTracker[i].length; j++){
milesTracker[i][j] = scnr.nextInt();
}
}

/* Answer goes here*/
  
  
System.out.println("Min miles: " + minMiles);
System.out.println("Max miles: " + maxMiles);
}
}

A study was conducted to see how people reacted to certain facial expressions. A sample group of n=36n=36 was randomly divided into six groups. Each group was assigned to to view one picture of a person making a facial expression. Each group saw a different picture, and the different expressions were (1) Surprised (2) Nervous (3) Scared (4) Sad (5) Excited (6) Angry. After viewing the pictures, the subjects were asked to rank the degree of dominance they inferred from the facial expression they saw. (The scale ranged from -10 to 10) The data collected is summarized in the table below.

Complete the following ANOVA table

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 2 decimals).
   y =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )
   
   Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?

Some people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane.

Do the data support that different octanes produce different miles per gallon at the α=0.02α=0.02 level of significance? Note: A normal probability plot of difference in car mileage between Octane 87 and Octane 92 indicates the population could be normal and a boxplot indicated no outliers.

a. Express the null and alternative hypotheses in symbolic form for this claim. Assume μ¯d=μ1−μ2,μd¯=μ1-μ2, where μ1μ1 is the population mean mileage for Octane 87 and μ2μ2 is the mean mileage for Octane 92.

1) H0:μd¯

2) H1:μd¯

b. What is the significance level?

α=

c. What is the test statistic? Round to 3 decimal places.

d. What is the p -value? Round to 5 decimal places.

e. Make a decision.

• Reject the null
• Do not reject the null

f. What is the conclusion?

• There is sufficient evidence to support the claim that different octanes produce different miles per gallon.
• There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.