Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.53 pounds and a standard deviation of 3.16 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.  

b) Let X represent the weight of a randomly selected bag. For what value of c is P(E(X) - c < X < E(X) + c)=0.96? Give your answer to four decimal places.  

c) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 17 that weigh greater than 50 lbs? Give your answer to four decimal places.  

d) Assuming the weights of individual bags are independent, what is the probability that 8 or fewer bags weigh greater than 50 pounds in a sample of size 17? Give your answer to four decimal places.  

Q. It was thought that at a particular point in time 15% of the rabbit population in a region was infected by RHDV1-K5 virus. At the time a researcher trapped 25 rabbits from this region and had each tested to see if it carries virus. The number of rabbits in this sample with the virus is denoted by V.

a) Write down the possible values of V.

b) State a suitable distribution for V and provide the parameter(s) for the distribution.

c) Determine the Expected value of V and interpret this value in context to the research.

d) USe and show manual calculation to determine the probability that at least 2 rabbits have the virus.

e) It transpired that 20 of the rabbit did in fact carry the virus. Use R commander to determine the probability that 20 or more rabbit will have the virus.

f) Considering your answer to part e), say if this casts doubt on the original understanding of the prevalence of the virus in this region at that point in time. Give brief explanation.  

A) The table below shows the results of a survey that asked 1052 adults from a certain country if they would support a change in their​ country's flag. A person is selected at random. Complete parts​ (a) through​ (d).

	Support	Oppose	Unsure	Total
Males	151	332	10	493
Females	244	296	19	559
Total	395	628	29	1052

​(a) Find the probability that the person opposed the change or is female.

​(b) Find the probability that the person supports the change or is male.

​(c) Find the probability that the person is not unsure or is female.

(d) Are the events​ "being male" and​ "support" mutually​ exclusive? Explain.

A.​No, because one​ can't be male and support the change at the same time.

B.​No, because there are 151 males that support the change.

C.​Yes, because there are 151 males that support the change.

D.​Yes, because one​ can't be male and support the change at the same time

B) The table below shows the results of a survey that asked 2859 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts​ (a) through​ (e).

	Frequently	Occasionally	Not at all	Total
Male	227	458	796	1481
Female	202	430	746	1378
Total	429	888	1542	2859

​(a) Find the probability that the person is frequently or occasionally involved in charity work.

​(b) Find the probability that the person is female or not involved in charity work at all.

​(c) Find the probability that the person is male or frequently involved in charity work.

​(d) Find the probability that the person is female or not frequently involved in charity work.

​(e) Are the events​ "being female" and​ "being frequently involved in charity​ work" mutually​ exclusive? Explain.

A.​No, because no females are frequently involved in charity work.

B.​Yes, because 202 females are frequently involved in charity work.

C.​No, because 202 females are frequently involved in charity work.

D.​Yes, because no females are frequently involved in charity work.

C) The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts​ (a) through​ (d).

	Nursing majors	​Non-nursing majors	Total
Males	99	1018	1117
Females	600	1727	2327
Total	699	2745	3444

(a) Find the probability that the student is male or a nursing major.

(b) Find the probability that the student is female or not a nursing major.

​(c) Find the probability that the student is not female or a nursing major.

​(d) Are the events​ "being male" and​ "being a nursing​ major" mutually​ exclusive? Explain.

A.​Yes, because there are 99 males majoring in nursing.

B.​No, because there are 99 males majoring in nursing.

C.Yes, because one​ can't be male and a nursing major at the same time.

D.​No, because one​ can't be male and a nursing major at the same time.

7. Approximately 20% of U.S. workers are afraid that they will never be able to retire. Suppose 10 workers are randomly selected. What is the probability that none of the workers is afraid that they will never be able to retire? a. 0.095 b. 0.995 c. 0.1074 d. 0.1228

8. According to WSJ, about 30% of adults have 4 year college degrees. Out of five randomly selected adults, what’s the probability that three have college degrees? a. 0.13 b. 0.15 c. 0.17 d. 0.19

9. According to WSJ, about 30% of adults have 4 year college degrees. Out of five randomly selected adults, what’s the probability that four have college degrees? a. 0.028 b. 0.132 c. 0.360 d. 0.868

10. According to WSJ, about 30% of adults have 4 year college degrees. Out of five randomly selected adults, what’s the probability that five have college degrees? a. 0.001 b. 0.002 c. 0.003 d. 004

11. According to WSJ, about 30% of adults have 4 year college degrees. Out of five randomly selected adults, what’s the probability that AT LEAST 3 out of 5 have college degrees? a. 0.183 b. 0.174 c. 0.162 d. 0.158  

12. A bank manager estimates that an average of two customers enters the tellers' queue every five minutes. Assume that the number of customers that enters the tellers' queue is Poisson distributed. What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period? a. 0.0034 b. 0.1033 c. 0.1377 d. 0.1606

13. The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2017 an average of three residential properties were auctioned off each weekday in the city of Boston. What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2017 in Boston? a. 0.1680 b. 0.1954 c. 0.2240 d. 0.8153

14. Particles (e.g. yeast cell) are suspended in a liquid medium at a concentration. A large volume of the suspension is thoroughly agitated, and then 1 ml is withdrawn. The concentration in this sample is 10 particles per ml. What is the probability that, in the entire liquid medium, the concentration is exactly 8 particles/ml? a. 0.0993 b. 0.1126 c. 0.8320 d. 0.0009

15. On average, 0.61 soldiers in each corp of the Prussian cavalry were kicked to death by horses each year. What is the probability that in the next year, exactly 3 soldiers will be kicked to death by a horse? a. 008 b. 0.01 c. 0.02 d. 0.03

16. Patients arrive at the emergency room of a hospital at the average rate of 6 per hour on weekend evenings. What is the probability of 4 arrivals in 30 minutes on a weekend evening? a. 0.152 b. 0.168 c. 0.174 d. 0.182

Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their own division’s return on investment (ROI). Assume the following information relative to the two divisions: Case 1 2 3 4 Alpha Division: Capacity in units 56,000 320,000 103,000 191,000 Number of units now being sold to outside customers 56,000 320,000 78,000 191,000 Selling price per unit to outside customers $ 99 $ 41 $ 68 $ 43 Variable costs per unit $ 60 $ 22 $ 43 $ 29 Fixed costs per unit (based on capacity) $ 24 $ 10 $ 26 $ 4 Beta Division: Number of units needed annually 10,600 65,000 19,000 62,000 Purchase price now being paid to an outside supplier $ 93 $ 39 $ 68 * — *Before any purchase discount. Required: 1. Refer to case 1 shown above. Alpha Division can avoid $3 per unit in commissions on any sales to Beta Division. a. What is Alpha Division's lowest acceptable transfer price? b. What is Beta Division's highest acceptable transfer price? c. What is the range of acceptable transfer prices (if any) between the two divisions? Will the managers probably agree to a transfer? 2. Refer to case 2 shown above. A study indicates that Alpha Division can avoid $4 per unit in shipping costs on any sales to Beta Division. a. What is Alpha Division's lowest acceptable transfer price? b. What is Beta Division's highest acceptable transfer price? c. What is the range of acceptable transfer prices (if any) between the two divisions? Would you expect any disagreement between the two divisional managers over what the exact transfer price should be? d. Assume Alpha Division offers to sell 65,000 units to Beta Division for $38 per unit and that Beta Division refuses this price. What will be the loss in potential profits for the company as a whole? 3. Refer to case 3 shown above. Assume that Beta Division is now receiving an 3% price discount from the outside supplier. a. What is Alpha Division's lowest acceptable transfer price? b. What is Beta Division's highest acceptable transfer price? c. What is the range of acceptable transfer prices (if any) between the two divisions? Will the managers probably agree to a transfer? d. Assume Beta Division offers to purchase 19,000 units from Alpha Division at $60.96 per unit. If Alpha Division accepts this price, would you expect its ROI to increase, decrease, or remain unchanged? 4. Refer to case 4 shown above. Assume that Beta Division wants Alpha Division to provide it with 62,000 units of a different product from the one Alpha Division is producing now. The new product would require $25 per unit in variable costs and would require that Alpha Division cut back production of its present product by 31,000 units annually. What is Alpha Division's lowest acceptable transfer price?

Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their own division’s return on investment (ROI). Assume the following information relative to the two divisions:

	Case
	1		2		3			4
Alpha Division:
Capacity in units		53,000		288,000		105,000			204,000
Number of units now being sold to outside customers		53,000		288,000		82,000			204,000
Selling price per unit to outside customers	$	99	$	43	$	67		$	45
Variable costs per unit	$	64	$	21	$	41		$	30
Fixed costs per unit (based on capacity)	$	24	$	13	$	25		$	7
Beta Division:
Number of units needed annually		9,700		74,000		19,000			60,000
Purchase price now being paid to an outside supplier	$	92	$	42	$	67	*		—

*Before any purchase discount.

Required:

1. Refer to case 1 shown above. Alpha Division can avoid $3 per unit in commissions on any sales to Beta Division.

a. What is Alpha Division's lowest acceptable transfer price?

b. What is Beta Division's highest acceptable transfer price?

c. What is the range of acceptable transfer prices (if any) between the two divisions? Will the managers probably agree to a transfer?

2. Refer to case 2 shown above. A study indicates that Alpha Division can avoid $4 per unit in shipping costs on any sales to Beta Division.

a. What is Alpha Division's lowest acceptable transfer price?

b. What is Beta Division's highest acceptable transfer price?

c. What is the range of acceptable transfer prices (if any) between the two divisions? Would you expect any disagreement between the two divisional managers over what the exact transfer price should be?

d. Assume Alpha Division offers to sell 74,000 units to Beta Division for $41 per unit and that Beta Division refuses this price. What will be the loss in potential profits for the company as a whole?

3. Refer to case 3 shown above. Assume that Beta Division is now receiving an 5% price discount from the outside supplier.

a. What is Alpha Division's lowest acceptable transfer price?

b. What is Beta Division's highest acceptable transfer price?

c. What is the range of acceptable transfer prices (if any) between the two divisions? Will the managers probably agree to a transfer?

d. Assume Beta Division offers to purchase 19,000 units from Alpha Division at $58.65 per unit. If Alpha Division accepts this price, would you expect its ROI to increase, decrease, or remain unchanged?

4. Refer to case 4 shown above. Assume that Beta Division wants Alpha Division to provide it with 60,000 units of a different product from the one Alpha Division is producing now. The new product would require $25 per unit in variable costs and would require that Alpha Division cut back production of its present product by 30,000 units annually. What is Alpha Division's lowest acceptable transfer price?

Suppose the manufacturer of a certain drug claims the adverse event rate of the drug is 20% (ie. 20% of people who take the drug have an adverse event), but you think the adverse event rate is higher. (In fact, you think the adverse event rate is 30%.) So, you want to do a study to show the adverse event rate is higher than 20%. If the adverse event rate is really 30% and you obtain a sample of size 10 patients, what is the power of your study for testing Ho: p=0.2 vs Ha: p > 0.2 with a significance level of 0.05? To address this question, answer the following: a) State in words what "power" means in the context of this problem. b) Determine the minimum number of adverse events among 10 patients that would need to happen to reject your null hypothesis. In other words, determine the minimum number of adverse events so that the one-sided p-value is less than 0.05. c) Now, calculate the probability of observing the number of events from part b or more events under the assumption that the true rate is 30%. In other words, calculate the power (the probability of rejecting the null hypothesis if the adverse event rate is really 0.3). d) Now do steps b) and c) to determine the power if the rate were really 70%. e) (*1 point) Compare the power in c) and d). This comparison illustrates (choose the best answer): i) power is higher with alternatives closer to the null hypothesis. ii) power is higher with alternatives farther from the null hypothesis. iii) power is higher with a smaller Type I error rate. iv) power is higher with a larger Type I error rate.

#define _CRT_SECURE_NO_WARNINGS

// Put your code below:

#include <stdio.h>

int main(void)
{
int day, hightemp[10], lowtemp[10], numbers, highesttemp, highestday, lowesttemp, lowestday, numbers2 = 0, hightotal = 0, lowtotal = 0, averageday = 0, numbers3;
double averagetemp;

printf("---=== IPC Temperature Calculator V2.0 ===---");

printf("\nPlease enter the number of days, between 3 and 10, inclusive: ");
scanf("%d", &numbers);

if (numbers < 3 || numbers > 10)

{
printf("\nInvalid entry, please enter a number between 3 and 10, inclusive: ");
scanf("%d", &numbers);
printf("\n");
}
while (numbers < 3 || numbers > 10);

for (day = 1; day <= numbers; day++)
{
printf("Day %d - High: ", day);
scanf("%d", &hightemp[day - 1]);

printf("Day %d - Low: ", day);
scanf("%d", &lowtemp[day - 1]);

if(highesttemp <= highesttemp[day - 1])
{
highesttemp = highesttemp[day - 1];
highesttemp = day;
}

if (lowesttemp >= lowesttemp[day - 1])
{
lowesttemp = lowesttemp[day - 1];
lowesttemp = day;
}
}
printf("\nDay Hi Low\n");
for (day = 1; day <= numbers; day++)
{
printf("%d %d %d\n", day, hightemp[day - 1], lowtemp[day - 1]);

}

printf("\nThe highest temperature was %d, on day %d\n", highesttemp, highestday);

printf("The lowest temperature was %d, on day %d\n", lowesttemp, lowestday);

while (numbers2 == 0)
{
printf("\nEnter a number between 1 and 5 to see average temperature for the entered number of days, enter a negative number to exit: ", numbers);
scanf("%d", &numbers3);

if (numbers3 < 0)
{
numbers2 = 1;
}
else
{

while (numbers3 <= 0 || numbers3 > numbers)
{
printf("\nInvalid entry, please enter a number between 1 and %dm inclusive: ", numbers);
scanf("%d", &numbers3);
}
hightotal = 0;
lowtotal = 0;

for (averageday = 1; averageday <= numbers3; averageday++)
{
hightotal += hightemp[averageday - 1];
lowtotal += lowtemp[averageday - 1];
}

averagetemp = (double) (hightotal + lowtotal) / (numbers3 * 2);

printf("\nThe average temperature up to day %d is: %.2lf", numbers3, averagetemp);
}
}
printf("\nGoodbye!");
return 0;
}

/////////////////////////////////////////////////////////////////////////

why is it not working?

1. A Linked List of Integers

File IntList.java contains definitions for a linked list of integers. The class contains an inner class IntNode that holds information for a single node in the list (a node has a value and a reference to the next node) and the following IntList methods:

• public IntList()—constructor; creates an empty list of integers
• public void addToFront(int val)—takes an integer and puts it on the front of the list
• public void addToEnd(int val)—takes an integer and puts it on the end of the list
• public void removeFirst()—removes the first value from the list
• public void print()—prints the elements in the list from first to last

File IntListTest.java contains a driver that allows you to experiment with these methods. Save both of these files to your directory, compile and run IntListTest, and play around with it to see how it works. Then add the following methods to the IntList class. For each, add an option to the driver to test it.

1. public int length()—returns the number of elements in the list
2. public String toString()—returns a String containing the print value of the list.
3. public void removeLast()—removes the last element of the list. If the list is empty, does nothing.
4. public void replace(int oldVal, int newVal)—replaces all occurrences of oldVal in the list with newVal.

Note that you can still use the old nodes; just replace the values stored in those nodes.

// ***************************************************************

// FILE: IntList.java

//

// Purpose: Defines a class that represents a list of integers

//

// ***************************************************************

public class IntList

{

private IntNode front; //first node in list

//-----------------------------------------

// Constructor. Initially list is empty.

//-----------------------------------------

public IntList()

{

front = null;

}

//-----------------------------------------

// Adds given integer to front of list.

//-----------------------------------------

public void addToFront(int val)

{

front = new IntNode(val,front);

}

//-----------------------------------------

// Adds given integer to end of list.

//-----------------------------------------

public void addToEnd(int val)

{

IntNode newnode = new IntNode(val,null);

//if list is empty, this will be the only node in it

if (front == null)

front = newnode;

else

{

//make temp point to last thing in list

IntNode temp = front;

while (temp.next != null)

temp = temp.next;

//link new node into list

temp.next = newnode;

}

}

//-----------------------------------------

// Removes the first node from the list.

// If the list is empty, does nothing.

//-----------------------------------------

public void removeFirst()

{

if (front != null)

front = front.next;

}

//------------------------------------------------

// Prints the list elements from first to last.

//------------------------------------------------

public void print()

{

System.out.println("--------------------");

System.out.print("List elements: ");

IntNode temp = front;

while (temp != null)

{

System.out.print(temp.val + " ");

temp = temp.next;

}

System.out.println("\n-----------------------\n");

}

//*************************************************************

// An inner class that represents a node in the integer list.

// The public variables are accessed by the IntList class.

//*************************************************************

private class IntNode

{

public int val; //value stored in node

public IntNode next; //link to next node in list

//------------------------------------------------------------------

// Constructor; sets up the node given a value and IntNode reference

//------------------------------------------------------------------

public IntNode(int val, IntNode next)

{

this.val = val;

this.next = next;

}

}

}

// ***************************************************************

// IntListTest.java

//

// Driver to test IntList methods.

// ***************************************************************

import java.util.Scanner;

public class IntListTest

{

private static Scanner scan;

private static IntList list = new IntList();

//----------------------------------------------------------------

// Creates a list, then repeatedly prints the menu and does what

// the user asks until they quit.

//----------------------------------------------------------------

public static void main(String[] args)

{

scan = new Scanner(System.in);

printMenu();

int choice = scan.nextInt();

while (choice != 0)

{

dispatch(choice);

printMenu();

choice = scan.nextInt();

}

}

//----------------------------------------

// Does what the menu item calls for.

//----------------------------------------

public static void dispatch(int choice)

{

int newVal;

switch(choice)

{

case 0:

System.out.println("Bye!");

break;

case 1: //add to front

System.out.println("Enter integer to add to front");

newVal = scan.nextInt();

list.addToFront(newVal);

break;

case 2: //add to end

System.out.println("Enter integer to add to end");

newVal = scan.nextInt();

list.addToEnd(newVal);

break;

case 3: //remove first element

list.removeFirst();

break;

case 4: //print

list.print();

break;

default:

System.out.println("Sorry, invalid choice")

}

}

//-----------------------------------------

// Prints the user's choices

//-----------------------------------------

public static void printMenu()

{

System.out.println("\n Menu ");

System.out.println(" ====");

System.out.println("0: Quit");

System.out.println("1: Add an integer to the front of the list");

System.out.println("2: Add an integer to the end of the list");

System.out.println("3: Remove an integer from the front of the list");

System.out.println("4: Print the list");

System.out.print("\nEnter your choice: ");

}

}