The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on time until the first engine overhaul.

b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

c. Based on part (a), are the signs of the regression coefficients logical?

d. What is the predicted time before the first engine overhaul for a particular truck driven 56,000 miles per year with an average load of 21 tons, an average driving speed of 59 mph, and 22,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

1.         Corey is the city sales manager for “RIBS,” a national fast food franchise. Every working day, Corey drives his car as follows:

                                                Miles

Home to office                           20

Office to RIBS No. 1                 15

RIBS No. 1 to No. 2                    8

RIBS No. 2 to No. 3                    3

RIBS No. 3 to office                  10

Office to home                           20

Corey’s deductible daily mileage is:

a.         0 miles.

b.         36 miles.

c.         46 miles.

d.         56 miles.

e.         76 miles.

2.         Which of the following trips, if any, will qualify for the travel expense deduction?

a.         Dr. Jones, a general dentist, attends a two-day seminar on financial planning.

b.         Dr. Brown, an undergraduate pre-med student, attends a two-day seminar on developing a medical practice.

c.         Paul, a romance language high school teacher, spends summer break in France, Portugal, and Spain improving his language skills.

d.         Myrna went on a two-week vacation in Boston. While there, she visited her employer’s home office to have lunch with former co-workers.

e.         Mary, a CPA, attends a three-day seminar on state income taxation.

3.         Tax advantages of being self-employed (rather than being an employee) include:

a.         The self-employment tax is always lower than the Social Security tax.

b.         The overall limitation (50%) on meals does not apply.

c.         An office in the home deduction from AGI is available without having to meet the “convenience of the employer” test.

d.         Job-related expenses are deductions for AGI.

e.         Both (c) and (d) are advantages.

4.         When using the automatic mileage method, which of the following expenses, if any, also can be claimed?

a. Engine tune-up.

b. Parking.

c. Interest on automobile loan.

d. MACRS depreciation.

e. None of these.

5.         Which, if any, of the following is subject to a 50% cutback adjustment for the cost of meals in 2019?

a.         An airline pilot for an executive jet rental company who pays his own travel expenses while away from home on flights she pilots.

b.         Meals provided at cost to employees by a cafeteria funded by the employer/taxpayer.

c.         A Fourth of July company picnic for employees of the employer/taxpayer.

d.         A vacation trip to Bermuda awarded to the employer/taxpayer’s top salesperson, where the cost (including meals) is treated as a taxable bonus to the employee.

e.         None of these is subject to the 50% cutback.

1) Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41.

(a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224.

Round your answer to the nearest integer.
The value of   x is_______

(b) Find the value of x so that the area under the normal curve to the right of x is 0.3745.

Round your answer to the nearest integer.
The value of   x is ______

2) A study has shown that 24% of all college textbooks have a price of $80 or higher. It is known that the standard deviation of the prices of all college textbooks is $10.00. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Round your answer to the nearest integer.

μ=

3) Use a table, calculator, or computer to find the specified area under a standard normal curve.

Round your answers to 4 decimal places.

a) More than a z-score of 2.48; area = _____________

b) More than a z-score of 1.7; area =_____________

c) More than a z-score of -0.41; area = _____________

d) More than a z-score of 00; area = _____________

4)

The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at  1-mile intervals. After the police officers observe how long a car takes to cover the mile, a computer estimates that cars speed. Assume that the errors of these estimates are normally distributed with a mean of  0 and a standard deviation of  3.58 miles per hour.

a. The state police chief has directed his officers not to issue a speeding citation unless the aerial units estimate of speed is at least 66 miles per hour. What is the probability that a car travelling at 61 miles per hour or slower will be cited for speeding?

Round your answer to four decimal places.

The probability that a car travelling at 61 miles per hour or slower will be cited for speeding is ______

b. Suppose the chief does not want his officers to cite a car for speeding unless they are 99% sure that it is travelling at 61 miles per hour or faster. What is the minimum estimate of speed at which a car should be cited for speeding?

Round your answer to the nearest integer.

The minimum estimate of speed is __

Part 1.

3.13 Overweight baggage: Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 44.8 pounds and standard deviation 3.3 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee. (Round to the nearest percent.) __________.

Part 2.

There are two distributions for GRE scores based on the two parts of the exam. For the verbal part of the exam, the mean is 151 and the standard deviation is 7. For the quantitative part, the mean is 153 and the standard deviation is 7.67. Use this information to compute each of the following:
(Round to the nearest whole number.)

a) The score of a student who scored in the 80-th percentile on the Quantitative Reasoning section. ________.
b) The score of a student who scored worse than 65% of the test takers in the Verbal Reasoning section. ________.

Part 3.

3.10 Heights of 10 year olds: Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 56 inches and standard deviation 5 inches.

a) What is the probability that a randomly chosen 10 year old is shorter than 47 inches? (Keep 4 decimal places.) ____________.
b) What is the probability that a randomly chosen 10 year old is between 60 and 66 inches? (Keep 4 decimal places.) __________.
c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"? (Keep 2 decimal places.) ________. inches
d) The height requirement for Batman the Ride at Six Flags Magic Mountain is 55 inches. What percent of 10 year olds cannot go on this ride? (Keep 2 decimal places.) %_______.

Part 4.

3.12 Speeding on the I-5, Part I: The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.1 miles/hour and a standard deviation of 5 miles/hour. (Keep 2 decimal places.)

a) What percent of passenger vehicles travel slower than 80 miles/hour? _________%
b) What percent of passenger vehicles travel between 60 and 80 miles/hour? ____________%
c) How fast do the fastest 5% of passenger vehicles travel? __________ miles/hour
d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5. __________%

8.16 LAB: Mileage tracker for a runner

Given the MileageTrackerNode class, complete main() to insert nodes into a linked list (using the InsertAfter() function). The first user-input value is the number of nodes in the linked list. Use the PrintNodeData() function to print the entire linked list. DO NOT print the dummy head node.

Ex. If the input is:

3
2.2
7/2/18
3.2
7/7/18
4.5
7/16/18

the output is:

2.2, 7/2/18
3.2, 7/7/18
4.5, 7/16/18

_____________________________

The given code that i need to use is:

______________________________

Main.cpp

#include "MileageTrackerNode.h"
#include <string>
#include <iostream>
using namespace std;

int main (int argc, char* argv[]) {
// References for MileageTrackerNode objects
MileageTrackerNode* headNode;
MileageTrackerNode* currNode;
MileageTrackerNode* lastNode;

double miles;
string date;
int i;

// Front of nodes list
headNode = new MileageTrackerNode();
lastNode = headNode;

// TODO: Read in the number of nodes

// TODO: For the read in number of nodes, read
// in data and insert into the linked list

// TODO: Call the PrintNodeData() method
// to print the entire linked list

// MileageTrackerNode Destructor deletes all
// following nodes
delete headNode;
}

___________________________________________________

MileageTrackerNode.h

#ifndef MILEAGETRACKERNODEH
#define MILEAGETRACKERNODEH

#include <string>
using namespace std;

class MileageTrackerNode {
public:
// Constructor
MileageTrackerNode();

// Destructor
~MileageTrackerNode();

// Constructor
MileageTrackerNode(double milesInit, string dateInit);

// Constructor
MileageTrackerNode(double milesInit, string dateInit, MileageTrackerNode* nextLoc);

/* Insert node after this node.
Before: this -- next
After: this -- node -- next
*/
void InsertAfter(MileageTrackerNode* nodeLoc);

// Get location pointed by nextNodeRef
MileageTrackerNode* GetNext();

void PrintNodeData();

private:
double miles; // Node data
string date; // Node data
MileageTrackerNode* nextNodeRef; // Reference to the next node
};

#endif

______________________________________________

MileageTrackerNode.cpp

#include "MileageTrackerNode.h"
#include <iostream>

// Constructor
MileageTrackerNode::MileageTrackerNode() {
miles = 0.0;
date = "";
nextNodeRef = nullptr;
}

// Destructor
MileageTrackerNode::~MileageTrackerNode() {
if(nextNodeRef != nullptr) {
delete nextNodeRef;
}
}

// Constructor
MileageTrackerNode::MileageTrackerNode(double milesInit, string dateInit) {
miles = milesInit;
date = dateInit;
nextNodeRef = nullptr;
}

// Constructor
MileageTrackerNode::MileageTrackerNode(double milesInit, string dateInit, MileageTrackerNode* nextLoc) {
miles = milesInit;
date = dateInit;
nextNodeRef = nextLoc;
}

/* Insert node after this node.
Before: this -- next
After: this -- node -- next
*/
void MileageTrackerNode::InsertAfter(MileageTrackerNode* nodeLoc) {
MileageTrackerNode* tmpNext;

tmpNext = nextNodeRef;
nextNodeRef = nodeLoc;
nodeLoc->nextNodeRef = tmpNext;
}

// Get location pointed by nextNodeRef
MileageTrackerNode* MileageTrackerNode::GetNext() {
return nextNodeRef;
}

void MileageTrackerNode::PrintNodeData(){
cout << miles << ", " << date << endl;
}

The following equations describe an economy. (Think of C, I, G, etc., as being measured in billions and I as a percentage; a 5 percent interest rate implies I=5).

C = 0.8 (1 – t) Y

                              t = 0.30

                              I = 1000 – 50 i

G= 500

                              L = 0.25Y – 65 i

M/P = 700

1. Derive the IS equation.

AD = C + I + G + NX

AD = 0.8 (1 – t) Y + 1000 – 50i + 500

AD = 0.8 (1 – 0.3) Y + 1500 – 50i

             At equilibrium AD = Y so

                        Y= 0.8 (1 – 0.3) Y + 1500-50i

                        Y- [0.8 (1 - .3) Y]=1500 – 50i

                        Y[1 – (0.8(1 - .3))] = 1500 – 50i

                        Y= [1/ (1- (0.8 (1- 0.3))] x (1500- 50i)

                        Y= 2.27(1500 – 50i)

                        Y= 3405 – 113.5i

2. Derive the LM equation.

M-bar/P-bar = L

700= .25Y – 65i

0.25Y = 700 +65i

Y= 4(700 + 65i)

Y= 2800 + 260i

3. What are the equilibrium levels of income and interest rate?

3405 – 113.5i = 2800 + 260i

3405 – 2800 = 113.5i + 260i

605= 373.5i

i= 1.62

Y= 2800 + 260(1.62)

Y= 3221.2

4. What is the value of a_G which corresponds to simple multiplier with taxes?
   1. AG= 2.27 (First question)
5. What would be the new equilibrium levels of income and interest rate if the congress passed a tax-cut and the new tax rate was 25%, and concurrently, people became less frugal and consequently marginal propensity to consume increases to 0.90.
6. If the increased spending overshoots and the economy starts to experience inflation, calculate the new levels of equilibrium income and interest rate if the new Federal Reserve decided to curb spending and by lowering the real money supply to 550?
7. For each step, graph the IS and LM curves and clearly show their movements for the problems above. Although the graph needs not to be precise, you must clearly show if IS or LM curves shifted or tilted and in which direction.

1-A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 1750 square feet, find the maximum and minimum sizes of the homes the contractor should build. Assume that the standard deviation is 96 square feet and the variable is normally distributed.

2-Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 13, p = 0.7, P(Fewer than 4)

3-A student takes a 5 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 2 questions correct?

4- An investor is considering a $15,000 investment in a start-up company. She estimates that she has probability 0.15 of a $10,000 loss, probability 0.1 of a $10,000 profit, probability 0.3 of a $30,000 profit, and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit? $11,500 $15,250 $10,000 $8,500

Since you became an expert in Corporate Finance and CAPM, now you want to make some money by investing in stocks. Instead of buying one stock, you will make a diversified portfolio using several stocks. Suppose that there are only 3 stocks in the market, and expected return, standard deviation, and correlations are as follows

Stocks Expected Return Standard Deviation

Stock A    5% 5%

Stock B    7% 10%

Stock C 10%    20%

Correlations Stock A Stock B Stock C

Stock A 1    0.4 -0.3

Stock B 0.4 1 0.7

Stock C -0.3 0.7 1

*Calculate Expected Return and Standard Deviation of Each Portfolio:
Portfolio 1: 30% in Stock A + 70% in Stock B
Portfolio 2: 60% in Stock B + 40% in Stock C
Portfolio 3: 50% in Stock A + 50% in Stock C

You are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.]

P = [0.6 0 0.4

1 0 0

0 0.2 0.8]