- What is the difference between the Relative Frequency Approximation of Probability and the Classical Approach to Probability? What happens when a procedure is repeated again and again?
- The probability of a certain event can't be greater than 1 or less than zero. Why not?
- What is a compound event? Describe the difference between P(A or B) and P(A and B)?
- What is a complementary event? What is the sum of the probability of A and the probability of the complement of A?
- What is a random variable and what is a probability
distribution? Describe the difference between continuous random
variables and discrete random variables? Provide an example of
each.
- What are the main parameters of a probability distribution?
- How we can use the mean and the standard deviation to calculate the maximum and minimum significant values?
- Recall the definition of a complementary event, and explain your understanding of a binomial probability distribution.
- What is the formula used to calculate the probability of a single event in binomial probability distribution?
- For binomial distributions, there are 3 very simple formulas used to calculate the mean, variance and standard deviation. List these 3 formulas.
Directions: Once the forum opens on Day 1, you are required to “Start a New Thread” by Day 3. Initial post should be 200-300 words, not counting citations. Remember to cite your sources properly. Label your post with a provocative/descriptive title that invites your
In: Statistics and Probability
The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 70,000 | $ | 38.00 | $ | 4.70 | $ | 3.50 |
| Trish | 62,000 | $ | 4.60 | $ | 1.60 | $ | 1.00 |
| Sarah | 55,000 | $ | 31.00 | $ | 9.44 | $ | 6.50 |
| Mike | 48,000 | $ | 14.00 | $ | 4.00 | $ | 4.50 |
| Sewing kit | 345,000 | $ | 10.00 | $ | 5.20 | $ | 0.50 |
The following additional information is available:
The company’s plant has a capacity of 94,500 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $10 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $585,000 per year. Variable overhead costs are $3 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 94,500 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
How many direct labor hours are used to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
What is the contribution margin per direct labor-hour for each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? (Do not round intermediate calculations. Round your final answer to a whole dollar amount.)
|
Assuming that the company has made optimal use of its 94,500 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
In: Accounting
The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 70,000 | $ | 38.00 | $ | 4.70 | $ | 3.50 |
| Trish | 62,000 | $ | 4.60 | $ | 1.60 | $ | 1.00 |
| Sarah | 55,000 | $ | 31.00 | $ | 9.44 | $ | 6.50 |
| Mike | 48,000 | $ | 14.00 | $ | 4.00 | $ | 4.50 |
| Sewing kit | 345,000 | $ | 10.00 | $ | 5.20 | $ | 0.50 |
The following additional information is available:
The company’s plant has a capacity of 94,500 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $10 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $585,000 per year. Variable overhead costs are $3 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 94,500 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
How many direct labor hours are used to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
What is the contribution margin per direct labor-hour for each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? (Do not round intermediate calculations. Round your final answer to a whole dollar amount.)
|
Assuming that the company has made optimal use of its 94,500 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
In: Accounting
The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 68,000 | $ | 31.00 | $ | 4.50 | $ | 4.20 |
| Trish | 60,000 | $ | 5.00 | $ | 1.40 | $ | 0.77 |
| Sarah | 53,000 | $ | 44.50 | $ | 9.14 | $ | 6.30 |
| Mike | 34,000 | $ | 17.00 | $ | 3.80 | $ | 4.90 |
| Sewing kit | 343,000 | $ | 9.80 | $ | 5.00 | $ | 0.42 |
The following additional information is available:
The company’s plant has a capacity of 127,580 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $7 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $565,000 per year. Variable overhead costs are $5 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 127,580 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
How many direct labor hours are used to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
What is the contribution margin per direct labor-hour for each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
ssuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? (Do not round intermediate calculations. Round your final answer to a whole dollar amount.)
|
Assuming that the company has made optimal use of its 127,580 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
|
In: Accounting
The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 57,000 | $ | 23.00 | $ | 5.00 | $ | 1.50 |
| Trish | 49,000 | $ | 7.00 | $ | 1.80 | $ | 0.60 |
| Sarah | 42,000 | $ | 41.00 | $ | 7.49 | $ | 3.00 |
| Mike | 45,500 | $ | 10.00 | $ | 2.70 | $ | 2.00 |
| Sewing kit | 332,000 | $ | 8.70 | $ | 3.90 | $ | 0.35 |
The following additional information is available:
The company’s plant has a capacity of 80,520 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $5 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $590,000 per year. Variable overhead costs are $2 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 80,520 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
3. What is the contribution margin per direct labor-hour for each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? (Do not round intermediate calculations. Round your final answer to a whole dollar amount.)
|
5. Assuming that the company has made optimal use of its 80,520 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
In: Accounting
The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company’s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:
| Product | Demand Next year (units) |
Selling Price per Unit |
Direct Materials |
Direct Labor |
|||
| Debbie | 69,000 | $ | 41.00 | $ | 4.60 | $ | 4.00 |
| Trish | 61,000 | $ | 4.50 | $ | 1.50 | $ | 1.00 |
| Sarah | 54,000 | $ | 30.50 | $ | 9.29 | $ | 7.00 |
| Mike | 46,800 | $ | 15.00 | $ | 3.90 | $ | 5.00 |
| Sewing kit | 344,000 | $ | 9.90 | $ | 5.10 | $ | 0.50 |
The following additional information is available:
The company’s plant has a capacity of 100,400 direct labor-hours per year on a single-shift basis. The company’s present employees and equipment can produce all five products.
The direct labor rate of $10 per hour is expected to remain unchanged during the coming year.
Fixed manufacturing costs total $575,000 per year. Variable overhead costs are $2 per direct labor-hour.
All of the company’s nonmanufacturing costs are fixed.
The company’s finished goods inventory is negligible and can be ignored.
Required:
1. How many direct labor hours are used to manufacture one unit of each of the company’s five products?
2. How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products?
3. What is the contribution margin per direct labor-hour for each of the company’s five products?
4. Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?
5. Assuming that the company has made optimal use of its 100,400 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)?
1... How many direct labor hours are used to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
2... How much variable overhead cost is incurred to manufacture one unit of each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
3... What is the contribution margin per direct labor-hour for each of the company’s five products? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
4... Assuming that direct labor-hours is the company’s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource? (Do not round intermediate calculations. Round your final answer to a whole dollar amount.)
|
5... Assuming that the company has made optimal use of its 100,400 direct labor-hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity (that is, for added direct labor time)? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
|
In: Accounting
Bobsy the Human Pretzel, a world-famous contortionist, entered into a contract on December 1, 2018 to perform at the Omaha State Fair during the month of January, 2019. Alan, the organizer of the fair, advertised that Bobsy would be performing and received purchases for many tickets to the Omaha State Fair in advance. In December 10, 2018, Noland, the owner and director of the “Museum of the Strange and Unusual,” knew of Bobsy’s contract with Alan, and offered Bobsy more money and a private jet, among other things, to convince Bobsy to perform at his museum in January, 2019 instead of performing at the Omaha State Fair. On December 15, 2018, Bobsy contacted Alan and told him that he would not be performing at the State Fair but would be performing at the “Museum of the Strange and Unusual” instead. After Alan found out this information, he filed suit against Bobsy.
(a) If Alan sued Bobsy, demanding specific performance of the contract, who wins? Explain fully.
(b) If Alan sought an injunction against Bobsy to stop him from performing at the Museum of the Strange and Unusual, who wins? Explain fully.
(c) If Alan sued Bobsy for breach of contract and demands damages, what damages if any, may Alan recover?
(d) After Bobsy sorts out the legal issues with the Omaha State Fair, he signs a contract with the Museum of the Strange and Unusual to perform in April, 2019. While in the shower, Bobsy decides to prepare for the show by performing the very basic contortionist move, “back bend ending in pretzel.’ He slips and breaks one of his legs and severely injures his back. (side note: a contortionist is an entertainer who twists and bends their body into strange and unnatural positions.) After being stabilized in the hospital, Bobsy immediately contacts Noland and tells him what happened. Noland tells Bobsy, “Sorry to hear that, its going to be very hard for you to perform with those injuries. Can’t wait to see you pull it off!” When Bobsy refuses to abide by the contract, Noland sues Bobsy for breach of contract, judgment for whom? Explain fully.
In: Operations Management
Consider the probability that exactly 95 out of 158 computers will not crash in a day. Assume the probability that a given computer will not crash in a day is 56%. Approximate the probability using the normal distribution.
In: Statistics and Probability
How do you write pseudocode for this problem? The decides are provided below.
Problem Statement
We are going to create a game called TwentyOne, which is similar to the Blackjack and War card games. This game has a dealer/computer and 1-4 players, and the game will generate random numbers from 1 to 11 to simulate the values in cards. All players start with a specified amount of money, which they determine at the start of the game, and the goal is to see if you can get closer than the dealer to twenty-one points without going over.
With each player’s turn, they first bet against the dealer, and then play against the dealer before moving on to the next player. An initial random number, 1-11, is generated, and after each random number is generated, the player decides whether they want to generate another to add to their total points trying to get as close to 21 as possible without going over. The dealer is also given random numbers, but the strategy you use for determining whether they get another random number is your choice. The rules for the game play are below.
• If the player busts, the player automatically loses their bet, and the dealer doesn’t need to play against that player.
• If the player gets exactly 21 in hand, the player automatically wins their bet, and the dealer doesn’t need to play.
• If the dealer busts, the player automatically wins their bet.
• If the dealer ties with the player, then the player doesn’t win or lose their bet. • If the player’s bet is more than their bank, then you need to continue to re-prompt for a new bet until a good value is given.
• If a player’s bank is 0, they get skipped.
• If all players’ banks are 0, then the game is automatically over!
• After all players take a turn against the dealer, then the players can collectively cash out or play again.
Example gameplay below (User inputs are highlighted):
How many players do you have (1-4)? 3
Player 1, how much money are you starting with? 20
Player 2, how much money are you starting with? 50
Player 3, how much money are you starting with? 30
Player 1’s turn…
Player 1, how much do you bet you can beat the dealer? 10
Player 1, you got a(n) 10. Your running total is 10. Do you want another number (0-no or 1-yes)? 1
Player 1, you got a(n) 8. Your running total is 18. Do you want another number (0-no or 1-yes)? 0
Your total points are 18.
Dealer’s turn…
The dealer gets a(n) 11, running total is 11.
The dealer gets a(n) 11, running total is 22.
The dealer busts! You win!
Player 1 has 30.00.
Player 2’s turn…
Player 2, how much do you bet you can beat the dealer? 50
Player 2, you got a(n) 8. Your running total is 8. Do you want another number (0-no or 1-yes)? 1
Player 2, you got a(n) 9. Your running total is 17. Do you want another number (0-no or 1-yes)? 0
Your total points are 17.
The dealer gets a(n) 11, running total is 11.
The dealer gets a(n) 10, running total is 21.
The dealer stops…
The dealer has 21 points. You lose!
Player 2 has 0.00.
Player 3’s turn…
Player 3, how much do you bet you can beat the dealer? 50
Invalid number, you only have 30 in hand.
Player 3, how much do you bet you can beat the dealer? 25
Player 3, you got a(n) 8. Your running total is 8. Do you want another number (0-no or 1-yes)? 1
Player 3, you got a(n) 9. Your running total is 17. Do you want another number (0-no or 1-yes)? 1
Player 3, you got a(n) 3. Your running total is 20. Do you want another number (0-no or 1-yes)? 0
Your total points are 20.
The dealer gets a(n) 10, running total is 10.
The dealer gets a(n) 10, running total is 20.
The dealer stops…
The dealer has 20 points. Tie game!
Player 3 has 30.00.
Do you want to play again (0-no or 1-yes)? 1
Player 1’s turn…
Player 1, how much do you bet you can beat the dealer? 10
Player 1, you got a(n) 10. Your running total is 10. Do you want another number (0-no or 1-yes)? 1
Player 1, you got a(n) 11. Your running total is 21.
You got 21 in hand. You win!
Player 1 has 40.00.
Player 2 is skipped…
Player 3’s turn…
Player 3, how much do you bet you can beat the dealer? 20
Player 3, you got a(n) 10. Your running total is 10. Do you want another number (0-no or 1-yes)? 1
Player 3, you got a(n) 9. Your running total is 19. Do you want another number (0-no or 1-yes)? 1
Player 3, you got a(n) 5. Your running total is 24.
You bust. You lose!
Player 3 has 10.00.
Do you want to play again (0-no or 1-yes)? 0
Program Design.
• What does the overall big picture of this program look like? (flowchart or pseudocode) What data/variables do you need to create, when do you read input from the user, what is the dealer strategy going to be? Can you reuse some of the variables? If so, what are they?
o What are the decisions that need to be made in this program?
o What tasks are repeated?
• What kind of bad inputs are you going to handle?
Based on your answers above, list the specific steps or provide a flowchart of what is needed to create this program to play TwentyOne. Be very explicit!!!
(10 pts) Extra Credit 1
Handle all bad user input, even data of the wrong type. i.e. Re-prompt the user if he/she enters “asdf” instead of 1 or 0.
(10 pts) Extra Credit 2
Change the game play so that the dealer plays against all players in a turn, rather than playing only again one player at a time.
In: Computer Science
The table below is a discrete probability distribution of study hours for mathematics in a given week.
|
Hours (x) |
1 |
2 |
3 |
4 |
5 |
|
P(x) |
0.16 |
0.22 |
? |
0.20 |
0.14 |
In: Statistics and Probability