Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:
| Supplier | |||
|---|---|---|---|
| Component | 1 | 2 | 3 |
| 1 | $12 | $12 | $11 |
| 2 | $10 | $12 | $10 |
Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:
| Supplier | 1 | 2 | 3 |
|---|---|---|---|
| Capacity | 600 | 1025 | 800 |
If the Edwards production plan for the next period includes 1000 units of component 1 and 775 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".
| Supplier | |||
|---|---|---|---|
| 1 | 2 | 3 | |
| Component 1 | |||
| Component 2 | |||
What is the total purchase cost for the components? Round your answer to the nearest dollar.
$
In: Math
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 68 wpm and standard deviation 17 wpm.
What is the probability that a randomly selected typist's speed is at most 68 wpm?
What is the probability that a randomly selected typist's speed is less than 68 wpm?
What is the probability that a randomly selected typist's speed is between 34 and 85 wpm? (Round your answer to four decimal places.)
Would you be surprised to find a typist in this population whose speed exceeded 119 wpm? (Round your numerical value to four decimal places.)
It would ---Select--- (be, not be) surprising to find a typist in this population whose speed exceeded 119 wpm because this probability is ________ , which is ---Select--- (very small, very large) .
Suppose that two typists are independently selected. What is the probability that both their typing speeds exceed 102 wpm? (Round your answer to three decimal places.)
Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify individuals for this training? (Round your answer to the nearest whole number.)
People with typing speeds of wpm and ---Select--- (above, below) would qualify for the training.
In: Math
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x', for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
| Age | 40 | 41 | 42 | 43 | 63 |
|---|---|---|---|---|---|
| Bone Density | 353 | 344 | 328 | 326 | 322 |
Table
Copy Data
Step 1 of 6:
Find the estimated slope. Round your answer to three decimal places.
Step 2 of 6:
Find the estimated y-intercept. Round your answer to three decimal places.
Step 3 of 6:
Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
Step 4 of 6:
Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.
Step 5 of 6:
Find the estimated value of y when x=42. Round your answer to three decimal places.
Step 6 of 6:
Find the value of the coefficient of determination. Round your answer to three decimal places.
In: Math
Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11. 1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places. 2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places. 3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.
In: Math
In: Math
Make a Frequency Distribution Chart for the following set of Data 50, 10, 25, 20, 20, 20, 50,100, 30, 15
In: Math
Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect. 23 40 27 56 52 34 42 61 68 45 83 (a) Compute the sample mean distance at which the bat first detects an insect. (Round your answer to three decimal places.) cm (b) Compute the sample variance and standard deviation for this data set. (Round your answers to two decimal places.) Variance?
Standard deviation?
In: Math
Helena Lorimer runs a set of ice cream cafes that sell mainly three flavors of ice cream: vanilla, chocolate, and strawberry. Hot weather and high demand have caused her to run short of the main ingredients: milk, sugar, and cream. She has decided to make the best assortment of ice cream quantities in these three flavors and ration out the deliveries to the cafes.
She has collected data on the profitability of the various flavors, availability of supplies, and the amounts of ingredients required for each flavor.
|
Flavor |
Profit per Gallon |
Usage/Gallon |
||
|
Milk (gal.) |
Sugar (lbs.) |
Cream (gal.) |
||
|
Chocolate |
$1.00 |
0.45 |
0.50 |
0.10 |
|
Vanilla |
$0.90 |
0.50 |
0.40 |
0.15 |
|
Strawberry |
$0.95 |
0.40 |
0.40 |
0.20 |
|
Max available |
200 |
150 |
60 |
|
She wants to determine the optimal product mix for the Lorimer ice cream.
Let x1 = the # of gallons of Chocolate ice cream made
x2 = the # of gallons of Vanilla ice cream made
x3 = the # of gallons of Strawberry ice cream made
Max Z = $1.00x1 + $0.90x2 + $0.95x3
Subject To:
|
0.45x1 + 0.50x2 + 0.40x3 |
≤ 200 gal |
Milk Supply Constraint |
|
0.50x1 + 0.40x2 + 0.40x3 |
≤ 150 lbs |
Sugar Supply Constraint |
|
0.10x1 + 0.15x2 + 0.20x3 |
≤ 60 gal |
Cream Supply Constraint |
|
x1 |
≥ 0 gallons |
x1 Non-negativity Constraint |
|
x2 |
≥ 0 gallons |
x2 Non-negativity Constraint |
|
x3 |
≥ 0 gallons |
x3 Non-negativity Constraint |
Use your Excel spreadsheet model to answer the following question. Select the answer that best fits what you got. The answer options are not in any particular order.
What is the value of the X2 decision variable at the optimal solution?
Select one:
a. X2 = 275 gallons
b. X2 = 220
c. X2 = 275
d. X2 = 220 gallons
e. X2 = 120
f. X2 = 300 gallons
g. X2 = 200
h. X2 = 300
i. X2 = 200 gallons
j. X2 = 120 gallons
In: Math
In: Math
Choose whether the following statements are true or false.
The null and alternative hypotheses should be written in terms of the sample statistic. TrueFalse
The test statistic is computed assuming that the null hypothesis is true. TrueFalse
The test statistic is usually equal to the sample statistic ?⎯⎯⎯⎯⎯ TrueFalse
The p-value is the probability that the null hypothesis is true. TrueFalse 19. The p-value is the probability that the alternative hypothesis is true. TrueFalse
If the p-value is smaller than the level of significance (?α) then the null hypothesis is rejected. TrueFalse
In: Math
In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below. 39 60 75 115 135 140 149 150 236 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1578 1700 1825 2000 What is the maximum possible amount that could be awarded under the "2-standard deviations rule"? (Round all intermediate calculations and the answer to three decimal places.)
In: Math
Zhaoxin needs to successfully complete a coding project that involves complex natural language processing algorithms. Zhaoxin must choose between three different Application Programming Interfaces (API), but is unsure which API is best for the project. Being a Statistician, he decides to collect data, then use random chance to make the final decision. He assigns a probability of 0.45 for PyTorch, 0.25 for Keras, and the rest to TensorFlow. Each API affects Zhaoxin chances of completing the project on time. Zhaoxin will complete the project on-time with a 75% chance if he selects PyTorch, a 55% chance if he selects Keras, and only a 35% chance if he selects TensorFlow.
a) Draw a well-labeled tree diagram to illustrate the above information.
b) What is the probability that Zhaoxin is late and used the TensorFlow API?
c) What is the probability that Zhaoxin is on-time?
d) If Zhaoxin selects Keras as the API, what is the probability that he is on time with the project?
e) If Zhaoxin is late with the project, what is the probability that he selected PyTorch as the API?
f) Is choice of API and project completion independent? Support your answer mathematically.
In: Math
You have a portfolio with two bonds worth $100 each. Each bond has a 4% probability of defaulting. If the bond defaults it is worth $0. If it does not default it is worth $100. Defaults are independent of each other. What is the 95% VaR of each bond, and of the portfolio?
In: Math
The proportion of people in a given community who have a certain disease is 0.01. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02.
a.Given that the test is positive, what is the probability that the person has the disease?
b.Given that the test is negative, what is the probability that the person does not have the disease?
c.For many medical tests, it is standard procedure to repeat the test when a positive signal is given. Assume that repeated medical tests are independent. What is the probability that the person has the disease given that two independent tests are positive?
In: Math