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 asingle die twice and add the total. Model 2: Simulate a combinedroll of two dice, giving a number from 2 through 12 withappropriate probabilities.

Part II

Chapter 4

Assignments

Exercise 1 & Exercise 3

Q1

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

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

Q3

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

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

Part III

After reading provide Excel Spreadsheet solution and anaswerquestion .   please Please answer the questions below andattached Excel Spreadsheet.   

  Chad operated anautomobile sales business. A major dealer in town offered Chad aone-time opportunity to help them sell some “trade-ins.” Under thisdeal (see table below), Chad could take one used car at a time fromthe dealer and try to sell it. If he sold it, he could takeanother. There were three cars they wanted Chad to try to sell. TheDealer concluded the offer as follows: “Chad, we have not dealtwith you before so we plan to proceed cautiously: I’m sure youunderstand. If you accept this deal, you must take the compactfirst. If you sell the compact, then you can choose either of theother 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’sSelling 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 tryingto sell the car, but risked not making the sale. What should he do?Carlie needed a personal computer (PC) for school but her budgetwas tight, so she decided on a used machine. After some searching,she was down to two possibilities. One she had found in a nationalfranchized computer store, where she could purchase the PC for $800with a one-year guarantee. But she was intrigued by a secondpossibility: a local charity store was offering a used machine thathad been donated (exactly the same model as in the store) for $500.Carlie talked to a computer repair specialist, who said theprincipal problem with this model of PC was the hard drive, whichwas prone to failure: he estimated that half of the PCs of thismodel and age would require a new drive. He offered to test thecomputer and check the condition of the drive for $60. If the drivewas no good, a new drive could be fitted for $300 and would beguaranteed for one year. He added a qualification that his testingwas not perfect: about 25% of drives that passed his testing failedsoon afterwards requiring a new drive ($300) plus a service chargeof $100 for diagnosing the problem.

Question2 Please answer the question below and attached ExcelSpreadsheet.  

Carlie needed a personal computer (PC) for school but her budgetwas tight, so she decided on a used machine. After some searching,she was down to two possibilities. One she had found in a nationalfranchized computer store, where she could purchase the PC for $800with a one-year guarantee. But she was intrigued by a secondpossibility: a local charity store was offering a used machine thathad been donated (exactly the same model as in the store) for $500.Carlie talked to a computer repair specialist, who said theprincipal problem with this model of PC was the hard drive, whichwas prone to failure: he estimated that half of the PCs of thismodel and age would require a new drive. He offered to test thecomputer and check the condition of the drive for $60. If the drivewas no good, a new drive could be fitted for $300 and would beguaranteed for one year. He added a qualification that his testingwas not perfect: about 25% of drives that passed his testing failedsoon afterwards requiring a new drive ($300) plus a service chargeof $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 asingle die twice and add the total. Model 2: Simulate a combinedroll of two dice, giving a number from 2 through 12 withappropriate probabilities.