Question

Part 1

Question 1

Develop two simulation models of tossing two six-sided dice (numbered 1 through 6 on the six faces).Model 1: Simulate rolling a single die twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities.

Part II

Chapter 4

Assignments

Exercise 1 & Exercise 3

Q1

A potato chip manufacturer was having problems with the Weights and Measures inspectors after the inspectors found some bags containing less than the required 42.5 grams (formerly 1.5 ounces) of chips. In response, the manufacturer had increased the weight setting on the bagging machines to 50 grams, but were now over-packing the bags and, consequently, giving away chips.A random sample of bags were taken off the line and the chips in the bags were carefully weighed, as shown below:

1.     What is the average weight of chips in a bag?
2.     What is the standard deviation of the chip weights?
3.     According to the three rules of thumb, how many bags per 1,000 are expected to be below the required minimum weight of 42.5 grams?
4.     Plot a histogram of the chip weights. Does the data appear to be well approximated by a normal distribution?
5.     Using the normal distribution approximation, how many bags per 1,000 are expected to be below the required minimum weight of 42.5 grams?
6.     What setting (mean chip weight) should be used to ensure that “almost all” the bags contain at least 42.5 grams of chips while minimizing the excess chips in the bags?

Q3

A package goods supplier designed a new package (“white”) that it thought was more appealing than its old package (“blue”). It conducted a 10-week trial of the two packages in selected “matched” stores with the results shown below (sales in thousands of dollars).

1. Is there any statistical evidence that one or other package leads to higher sales?

Part III

After reading provide Excel Spreadsheet solution and anaswer question .   please Please answer the questions below and attached Excel Spreadsheet.   

  Chad operated an automobile sales business. A major dealer in town offered Chad a one-time opportunity to help them sell some “trade-ins.” Under this deal (see table below), Chad could take one used car at a time from the dealer and try to sell it. If he sold it, he could take another. There were three cars they wanted Chad to try to sell. The Dealer concluded the offer as follows: “Chad, we have not dealt with you before so we plan to proceed cautiously: I’m sure you understand. If you accept this deal, you must take the compact first. If you sell the compact, then you can choose either of the other two, or you can end the deal. If you sell the second car, then you can take the third if you wish.”

Car                   Chad’s Commission (On Sale)            Chad’s Selling Costs                Chad’s Estimate of Probability of Sale

Compact         $900                                                   $600                                        ¾

Standard         $1,500                                                 $200                                        2/3

Luxury              $3,000                                                 $600                                       50/50

Questions.

If he took a car, Chad would incur the selling costs in trying to sell the car, but risked not making the sale. What should he do? Carlie needed a personal computer (PC) for school but her budget was tight, so she decided on a used machine. After some searching, she was down to two possibilities. One she had found in a national franchized computer store, where she could purchase the PC for $800 with a one-year guarantee. But she was intrigued by a second possibility: a local charity store was offering a used machine that had been donated (exactly the same model as in the store) for $500. Carlie talked to a computer repair specialist, who said the principal problem with this model of PC was the hard drive, which was prone to failure: he estimated that half of the PCs of this model and age would require a new drive. He offered to test the computer and check the condition of the drive for $60. If the drive was no good, a new drive could be fitted for $300 and would be guaranteed for one year. He added a qualification that his testing was not perfect: about 25% of drives that passed his testing failed soon afterwards requiring a new drive ($300) plus a service charge of $100 for diagnosing the problem.

Question2 Please answer the question below and attached Excel Spreadsheet.  

Carlie needed a personal computer (PC) for school but her budget was tight, so she decided on a used machine. After some searching, she was down to two possibilities. One she had found in a national franchized computer store, where she could purchase the PC for $800 with a one-year guarantee. But she was intrigued by a second possibility: a local charity store was offering a used machine that had been donated (exactly the same model as in the store) for $500. Carlie talked to a computer repair specialist, who said the principal problem with this model of PC was the hard drive, which was prone to failure: he estimated that half of the PCs of this model and age would require a new drive. He offered to test the computer and check the condition of the drive for $60. If the drive was no good, a new drive could be fitted for $300 and would be guaranteed for one year. He added a qualification that his testing was not perfect: about 25% of drives that passed his testing failed soon afterwards requiring a new drive ($300) plus a service charge of $100 for diagnosing the problem.

What should Carlie do

Develop two simulation models of tossing two six-sided dice (numbered 1 through 6 on the six faces).Model 1: Simulate rolling a single die twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities.

Answer 1

question 1

Here, we have to develop two simulation models of tossing two six sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. the probability of getting any number from 1 to 6 is given as .

let us see the two simulation models given as below:

MODEL 1

Here, we have to simulate rolling a single dice twice and add the total

the simulation model is given as below

Number at first draw	Number at second draw	Total
6	2	8
2	2	4
6	1	7
4	5	9
6	6	12
2	1	3
1	1	2
3	6	9
3	2	5
1	5	6
4	3	7
1	5	6
5	6	11
5	2	7
2	5	7
3	5	8
4	1	5
2	4	6
3	5	8
3	2	5
5	5	10
4	6	10
4	6	10
1	3	4
2	1	3
1	2	3
3	5	8
6	6	12
6	4	10
6	1	7
2	1	3
5	3	8
2	6	8
2	6	8
4	6	10
3	1	4
2	4	6
5	6	11
6	1	7
6	3	9
5	1	6
3	6	9
4	2	6
5	1	6
3	1	4
1	4	5
6	5	11
4	1	5
1	4	5

MODEL 2

Here, We have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data.

the simulation model is given as below:

First dice	Second dice	Total
3	1	4
6	2	8
6	5	11
5	6	11
4	3	7
1	3	4
1	5	6
6	5	11
6	3	9
4	2	6
1	66	7
2	1	3
3	3	6
5	5	10
4	5	9
6	4	10
4	5	9
1	3	4
6	2	8
2	3	5
3	1	4
2	5	7
1	2	3
5	5	10
6	6	12
5	6	11
1	3	4
1	3	4
6	1	7
2	2	4
2	3	5
3	2	5
2	6	8
5	4	9
6	3	9
4	1	5
1	5	6
4	4	8
1	6	7
1	4	5

for any doubt

comment

i can do one question at a time