The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 11.711.7 fluid ounces and a standard deviation of 0.30.3 fluid ounce. A drink is randomly selected. (a) Find the probability that the drink is less than 11.511.5 fluid ounces. (b) Find the probability that the drink is between 11.311.3 and 11.511.5 fluid ounces. (c) Find the probability that the drink is more than 12.312.3 fluid ounces. Can this be considered an unusual event? Explain your reasoning. (a) The probability that the drink is less than 11.511.5 fluid ounces is nothing. (Round to four decimal places as needed.) (b) The probability that the drink is between 11.311.3 and 11.511.5 fluid ounces is nothing. (Round to four decimal places as needed.) (c) The probability that the drink is more than 12.312.3 fluid ounces is nothing. (Round to four decimal places as needed.) Is a drink containing more than 12.312.3 fluid ounces an unusual event? Choose the correct answer below. A. NoNo, because the probability that a drink contains more than 12.312.3 fluid ounces is greater thangreater than 0.05, this event is notis not unusual. B. NoNo, because the probability that a drink contains more than 12.312.3 fluid ounces is less thanless than 0.05, this event is notis not unusual. C. YesYes, because the probability that a drink contains more than 12.312.3 fluid ounces is less thanless than 0.05, this event isis unusual. D. YesYes, because the probability that a drink contains more than 12.312.3 fluid ounces is greater thangreater than 0.05, this event isis unusual.
In: Statistics and Probability
I need to figure this out in rstudio how to calculate this for Binomial and Poisson Distributions
Type 2 diabetes is becoming increasingly prevalent among the American adult population. Currently, 9.4% of American adults have diabetes (Centers for Disease Control and Prevention News Release, July 18, 2017). Suppose that 1000 American adults are randomly chosen and tested for Type 2 diabetes.
Use R to find the following probabilities, assuming that the rate of type 2 diabetes is 9.4%. Your R script should contain the commands you used to compute the probability.
Place your answers in the appropriate places in the Word document. Provide at least 4 decimal places for all probabilities.
In: Statistics and Probability
1.A pollster surveys 100 people and asks them how many hot dogs they eat monthly. The result is a discrete random variable that has the following probability distribution.
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
|
p(x) |
0.15 | 0.58 | 0.15 | 0.04 | 0.02 |
(a)
Complete the missing value in the table.
|
x |
0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
|
p(x) |
0.15 | 0.58 | 0.15 | 0.04 | 0.02 |
(b)
What is the median of this discrete random variable?
(c)
What is the mean of this discrete random variable?
(d)
Suppose the number of calories in a hot dog has a mean of 190 calories, and the bun contains, on average, 110 calories. Calculate the expected number of calories consumed each month due to eating hot dogs. Assume that every hot dog is consumed with a bun.
calories
2.The day after Thanksgiving, many people start shopping for Christmas. Suppose that a store was selling video games at a discount. The store limited the number of games a customer could purchase to four games. Let
x = number
of video games purchased, per customer. The associated probabilities are found in the table.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
|
p(x) |
0.01 | 0.04 | 0.10 | 0.31 | 0.54 |
(a)
What is the median of this discrete random variable?
(b)
What is the mean of this discrete random variable?
(c)
As an incentive, if a customer buys x video games they will receive x2 "come-back dollars" which can be used to purchase items the next time they visit the store. What is the expected number of "come-back dollars" that will be received per customer on the sales of these games?
come-back dollars
In: Statistics and Probability
Another utilization of cash flow analysis is setting the bid price on a project. To calculate the bid price, we set the project NPV equal to zero and find the required price. Thus the bid price represents a financial break-even level for the project. Guthrie Enterprises needs someone to supply it with 146,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you $1,860,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years this equipment can be salvaged for $156,000. Your fixed production costs will be $271,000 per year, and your variable production costs should be $9.10 per carton. You also need an initial investment in net working capital of $136,000. The tax rate is 35 percent and you require a return of 12 percent on your investment. Assume that the price per carton is $16.60. Calculate the project NPV. What is the minimum number of cartons per year that can be supplied and still break even? What is the highest fixed costs that could be incurred and still break even?
In: Finance
Another utilization of cash flow analysis is setting the bid price on a project. To calculate the bid price, we set the project NPV equal to zero and find the required price. Thus the bid price represents a financial break-even level for the project. Guthrie Enterprises needs someone to supply it with 146,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you $1,860,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years this equipment can be salvaged for $156,000. Your fixed production costs will be $271,000 per year, and your variable production costs should be $9.10 per carton. You also need an initial investment in net working capital of $136,000. The tax rate is 35 percent and you require a return of 12 percent on your investment. Assume that the price per carton is $16.60. Calculate the project NPV. What is the minimum number of cartons per year that can be supplied and still break even? What is the highest fixed costs that could be incurred and still break even?
In: Finance
Mojo Industries tracks the number of units purchased and sold throughout each accounting period but applies its inventory costing method at the end of each period, as if it uses a periodic inventory system. Assume its accounting records provided the following information at the end of the accounting period, January 31. The inventory’s selling price is $14 per unit. Transactions Unit Cost Units Total Cost Inventory, January 1 $ 5.00 310 $ 1,550 Sale, January 10 (200 ) Purchase, January 12 5.50 360 1,980 Sale, January 17 (150 ) Purchase, January 26 6.50 80 520 Assuming that for Specific identification method (item 1d) the January 10 sale was from the beginning inventory and the January 17 sale was from the January 12 purchase. Required: 1. Compute the amount of goods available for sale, ending inventory, and cost of goods sold at January 31 under each of the following inventory costing methods: (Round your intermediate calculations to 2 decimal places and final answers to the nearest dollar amount.) 2-a. Of the four methods, which will result in the highest gross profit? 2-b. Of the four methods, which will result in the lowest income taxes?
In: Accounting
Meagher Solutions Inc. manufactures memory chips for personal computers. An activity analysis was conducted, and the following activity costs were identified with the manufacture and sale of memory chips:
a. Identify the cost of quality classification for each activity.
| Quality Activities | Activity Cost | Quality Cost Classification | |||
| Correct shipment errors | $150,000 | ||||
| Disposing of scrap | 95,000 | ||||
| Emergency equipment maintenance | 125,000 | ||||
| Employee training | 50,000 | ||||
| Final inspection | 80,000 | ||||
| Inspecting incoming materials | 60,000 | ||||
| Preventive equipment maintenance | 40,000 | ||||
| Processing customer returns | 90,000 | ||||
| Scrap reporting | 45,000 | ||||
| Supplier development | 15,000 | ||||
| Warranty claims | 250,000 | ||||
| Total | $1,000,000 | ||||
b. Prepare a cost of quality report. Assume that the sales for the period were $4,000,000. If required, round percents to one decimal place.
| Meagher Solutions Inc. | |||
| Cost of Quality Report | |||
| Quality Cost Classification |
Quality Cost | Percent of Total Quality Cost |
Percent of Total Sales |
| Prevention | $ | % | % |
| Appraisal | % | % | |
| Internal failure | % | % | |
| External failure | % | % | |
| Total | $ | % | % |
c. The category with the fewest number of quality activities is . Nearly fifty percent of the quality activity costs are . The highest single cost is warranty claims, which is a(n) . Disposing of scrap, emergency equipment maintenance, and scrap reporting are all .
In: Accounting
The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is, set the project NPV to zero and solve for the variable in question. Guthrie Enterprises needs someone to supply it with 153,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost $1,930,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years this equipment can be salvaged for $163,000. Your fixed production costs will be $278,000 per year, and your variable production costs should be $10.70 per carton. You also need an initial investment in net working capital of $143,000. The tax rate is 23 percent and you require a return of 10 percent on your investment. Assume that the price per carton is $17.30.
| a. |
Calculate the project NPV. |
| b. |
What is the minimum number of cartons per year that can be supplied and still break even? |
| c. |
What is the highest fixed costs that could be incurred and still break even? |
In: Finance
In this Task you will investigate the sampling distribution and model for the proportion of heads that may show up when a coin is tossed repeatedly. Toss the coins if you want, but it's much easier and faster to do a simulation!
1. Set up the calculator's or random number generator to simulate tossing a coin 25 times. (The easiest way to do this is to generate 0's and 1's with equal probability, with 1 representing heads. By adding up all the 0's and 1's you can effectively count the number of heads. Dividing that coin by the number of theses will get you ^P, the sample proportion of heads.)
2. Run 20 trials, recording all the sample proportions and make a histogram of the results.
3. Repeat your simulation, this time tossing the coin 100 times. Again make a histogram of twenty sample proportions.
4. Compare your two distributions of the proportions of heads observed in your simulations.
5. What should have happened? Describe the sampling model for 100 tosses.
6. Compare the actual distribution of your twenty sample proportions for 100 tosses to what the sampling model predicts.
7. Describe how your results might differ if you had 1000 trials of the simulation instead of only 20.
In: Statistics and Probability
The overall divorce rate (i.e., the number of divorces divided by the number of marriages) has fallen dramatically since the 1980s. Since the rate is calculated relative to the number of marriages, this cannot be chalked up to fewer marriages. People who get married today have a much higher likelihood of staying married relative to thirty years ago. How might you use our economic principles to explain this result? Explain.
In: Economics