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:

*Before any purchase discount.

Managers are free to decide if they will participate in any internal transfers. All transfer prices are negotiated.

Required:

1. Refer to case 1 shown above. Alpha Division can avoid $4 per unit in commissions on any sales to Beta Division.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 $6 per unit in shipping costs on any sales to Beta Division.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 $39 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 the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 21,000 units from Alpha Division at $61.50 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 58,000 units of a different product from the one Alpha Division is producing now. The new product would require $27 per unit in variable costs and would require that Alpha Division cut back production of its present product by 29,000 units annually. What is the lowest acceptable transfer price from Alpha Division’s perspective?

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:

*Before any purchase discount.

Managers are free to decide if they will participate in any internal transfers. All transfer prices are negotiated.

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 the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 $5 per unit in shipping costs on any sales to Beta Division.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 68,000 units to Beta Division for $37 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 6% price discount from the outside supplier.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 20,000 units from Alpha Division at $57.04 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 56,000 units of a different product from the one Alpha Division is producing now. The new product would require $29 per unit in variable costs and would require that Alpha Division cut back production of its present product by 28,000 units annually. What is the lowest acceptable transfer price from Alpha Division’s perspective?

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:

*Before any purchase discount.

Managers are free to decide if they will participate in any internal transfers. All transfer prices are negotiated.

Required:

1. Refer to case 1 shown above. Alpha Division can avoid $6 per unit in commissions on any sales to Beta Division.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 $5 per unit in shipping costs on any sales to Beta Division.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 68,000 units to Beta Division for $39 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 6% price discount from the outside supplier.

a. What is the lowest acceptable transfer price from the perspective of the Alpha Division?

b. What is the highest acceptable transfer price from the perspective of the Beta Division?

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 18,000 units from Alpha Division at $55.16 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 56,000 units of a different product from the one Alpha Division is producing now. The new product would require $27 per unit in variable costs and would require that Alpha Division cut back production of its present product by 28,000 units annually. What is the lowest acceptable transfer price from Alpha Division’s perspective?

Error detection/correction C

Objective:

To check a Hamming code for a single-bit error, and to report and correct the error(if any)

Inputs:

1.The maximum length of a Hamming code

2.The parity of the check bits (even=0, odd=1)

3.The Hamming code as a binary string of 0’s and 1’s

Outputs:

1.The original parity bits (highest index to lowest index, left to right)

2.The new parity bits (highest index to lowest index, left to right)

3.The bit-wise difference between the original parity bits and the new parity bits

4.The erroneous bit (if any)

5.The corrected Hamming code (if there was an error)

Specification:

The program checks a Hamming code for a single-bit error based on choosing from a menu of choices, where each choice calls the appropriate procedure, where the choices are:

1) Enter parameters

2)Check

Hamming code

3) Quit program

To use the Math library, use: “#include <math.h>” to access various functions, such as pow(base, exp), log(number), etc.To perform the XOR function, use the operator “^”.

To use the String library, use: “#include <string.h>” to access various functions, such as strlen(string) which returns an integer representing the

length of a string of characters.

If necessary, include the flag “-lm” when you compile i.e. gcc filename.c–lm to be able to utilize the math library.

skeleton:

#include <stdio.h>

#include <math.h>

#include <stdlib.h>

#include <string.h>

/* declare global var's including a dynamic array of characters to store

the Hamming code,

original parity bits, and new parity bits*/

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

void "OPTION 1"()

{

/* prompt for maximum length of hamming code and even/odd parity */

printf("\nEnter the maximum length of the Hamming code: ");

/* allocate memory for Hamming code */

return;

}

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

void "OPTION 2"()

{

/* declare local var's */

/* prompt for Hamming code */

/* calculate actual length of input Hamming code, number of parity bits,

and highest parity bit */

/* Allocate memory for original and new parity bits */

/* Map parity bits within Hamming code to original parity bit array */

/* Calculate new parity bits */

/* OUTER LOOP: FOR EACH PARITY BIT */

/* initialize parity bit to even/off parity */

/* MIDDLE LOOP: FOR EACH STATING BIT OF A CONSECUTIVE SEQUENCE */

/* INNER LOOP: FOR EACH BIT OF A SEQUENCE TO BE CHECKED */

/* ignore original parity bit */

/* update new parity bit value based on Hamming code bit

checked */

} /* END INNER LOOP */

/* Map new parity bit value to new parity bit array */

} /* END OUTER LOOP */

/* Calculate error bit by XORing original and new parity bits from

respective arrays, weighted properly */

/* Print original parity bits & new parity bits and bit-wise difference */

/* If error, correct the bit and print which bit is in error and corrected

Hamming code */

/* Else if no error, print message of no code bit error */

return;

}

/******************************* OPTIONAL ************************/

void "FREE MEMORY"()

{

/* If daynamic array representing Hamming code is not NULL, free the

memory */

return;

}

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

int main()

{

/* print menu of options, select user's choice, call appropriate

procedure, and loop until user quits */

return 1;

}

Please do not use abcdef as variable names

Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in terms of winning a game. You decide to look at football statistics to provide evidence of which variable is a stronger predictor of wins.

Part a) Develop a simple linear regression that compares wins to yards made. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part b) Develop a simple linear regression that compares wins against yards allowed. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part c) Which explanatory variable provides a better prediction of the response variable? Support your answer briefly by citing the appropriate diagnostics. Note: Use an alpha of .05 for both tests of significance. Be sure to show ALL steps of the hypothesis testing procedure

EXCEL DATA TO USE.

In a binomial distribution n = 10 and p = 0.30. Find the probabilities of the following events: (Round the final answers to 3 decimal places.)

a. x = 2.

Probability            

b. x ≤ 2 (the probability that x is equal to or less than 2).

Probability            

c. x ≥ 3 (the probability that x is equal to or greater than 3).

Probability            

Three cards are chosen at random from a standard deck of 52.

1. What is the probability that all three cards are hearts?

2. What is the probability that all three cards are even?

3. What is the probability that all three cards are hearts and even?

4. What is the probability that all three cards are not aces?

e) What is the probability of at least one ace?

The accompanying data are from an article. Each of 307 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not.

Suppose one of these 307 individuals is to be selected at random.

(a)

Find the following probabilities. (Round your answers to three decimal places.)

(i)

P(male)

(ii)

P(hybrid)

(iii)

P(hybrid|male)

(iv)

P(hybrid|female)

(v)

P(female|hybrid)

(b)

For each of the probabilities calculated in part (a), write a sentence interpreting the probability.

(i)

P(male)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

    The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(ii)

P(hybrid)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.  

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(iii)

P(hybrid|male)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(iv)

P(hybrid|female)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.

The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(v)

P(female|hybrid)

The probability that a randomly selected male Honda Civic owner purchased a hybrid.

The probability that a randomly selected female Honda Civic owner purchased a hybrid.  

  The probability that a randomly selected Honda Civic owner is male.

The probability that a randomly selected Honda Civic owner purchased a hybrid.

The probability that a randomly selected hybrid Honda Civic owner is female.

(c)

Are the probabilities

P(hybrid|male)

and

P(male|hybrid)

equal? If not, explain the difference between these two probabilities.

No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.

No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid.    

Yes, the probabilities are equal.

Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline's flight is fully booked on a particular day, and let F denote the event that the second airline's flight is fully booked on that same day. Suppose that P(E) = 0.7, P(F) = 0.6, and P(E ∩ F) = 0.56.

(a) Calculate P(E | F) the probability that the first airline's flight is fully booked given that the second airline's flight is fully booked. (Round your answer to three decimal places.)


(b) Calculate P(F | E). (Round your answer to three decimal places.)

The distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. A random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. Which of the following describes the sampling distribution of the sample mean for samples of size 100 ?

A

Skewed to the right with standard deviation 0.7 sibling

B

Skewed to the right with standard deviation less than 0.7 sibling

C

Skewed to the right with standard deviation greater than 0.7 sibling

D

Approximately normal with standard deviation 0.7 sibling

E

Approximately normal with standard deviation less than 0.7 sibling

The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85.

Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?

• Both distributions are approximately normal with mean 65 and standard deviation 3.5.

  A

• Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

  B

• Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

  C

• Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.

  D

• Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.

E

The distribution of wait times for customers at a certain department of motor vehicles in a large city is skewed to the right with mean 23 minutes and standard deviation 11 minutes. A random sample of 50 customer wait times will be selected. Let x¯W represent the sample mean wait time, in minutes. Which of the following is the best interpretation of P(x¯W>25)≈0.10 ?

• For a random sample of 50 customer wait times, the probability that the total wait time will be greater than 25 minutes is approximately 0.10.

  A

• For a randomly selected customer from the population, the probability that the total customer wait time will be greater than 25 minutes is approximately 0.10.

  B

• For a randomly selected customer from the population, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

  C

• For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 23 minutes is approximately 0.10.

  D

• For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

E

Answer only e) to h) problems a) to d) have the answer included

Problem 1: Relations among Useful Discrete Probability Distributions. A Bernoulli experiment consists of only one trial with two outcomes (success/failure) with probability of success p. The Bernoulli distribution

is

P (X = k) = p^kq^1-k, k=0,1

The sum of n independent Bernoulli trials forms a binomial experiment with parameters n and p. The binomial probability distribution provides a simple, easy-to-compute approximation with reasonable accuracy to hypergeometric distribution with parameters N, M and n when n/N is less than or equal to 0.10. In this case, we can approximate the hypergeometric probabilities by a binomial distribution with parameters n and p = M/N. Further, the Poisson distribution with mean μ = np gives an accurate approximation to binomial probabilities when n is large and p is small.

1. Suppose in a region in Saskatchewan, among a group of 20 adults with cancer, seven were physically abused during their childhood. A random sample of five adult persons is taken from this group. Assume that sampling occurs without replacement, and the random variable X represents the number of adults in the sample who were abused during their childhood period.

(a) Write the formula for p(x), the probability distribution of X. How this distribution is called?

P(X=x)=(5/x)(0.35)^x(1-0.35)^5-x

(b) Using the adequate formulas, find the mean and variance of X?

μ=1.75

variance = 1.1375

(c) Find the probabilities of all the possible values of X. Plot the histogram of X and try the locate the approximative value of the mean μ.

x 0 1 2 3 4 5

P(X=x): 0.116 0.3124 0.3364 0.1811 0.04877 0.005

(d) What is the probability that at least one person was abused during childhood?

0.884

Now suppose another survey in British Columbia reveals that among 180 adults with cancer, only 80 adults were abused in their childhood. Suppose again that a random sample of five adult persons is taken from this group without replacement and let denote by Y the random variable which represents the number of adults abused during their childhood period in the sample.

(e) Find the probabilities of all the possible values of Y and plot the histogram of Y. How do you compare this histogram with the histogram of X.

(f) Find the probabilities of all the possible values of Y using the formula for the binomial distribution with p = 80/180

as an approximation. Plot the histogram and compare it with the histogram obtained using the hypergeometric formula.

(g) Is the precedent approximation close enough? Why or why not?

(h) Calculate the mean and variance using both binomial and hypergeometric distributions, respectively. Provide a comparison and summarize your findings.