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.

A=

. Let W denote the row space for A.

(a) Find an orthonormal basis for W and for W⊥.

(b) Compute projW⊥(1 1 1 1 1 ).

Use the finite difference method and the indicated value of n to approximate the solution of the given boundary-value problem. (Round your answers to four decimal places.)

x²y'' + 3xy' + 5y = 0,    y(1) = 6,  y(2) = 0;  n = 8

Find an orthogonal matrix P that diagonalizes the following matrix A:

A is 3 by 3 matrix:
(3 1 0

1 -1 1

0 0 2)

If the sequence is increasing then it a) converges to its supremum b) diverges c) may converge to its supremum d) is bounded

if S= { 1/n - 1/m: n,m belongs to N } where N is the set of natural numbers then infimum and supremum of S respectively are a) -1and 1 b) 0,1 c)0,0 d)can not be determined

Please explain

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 3zj + 5yk, C is the curve of intersection of the plane x + z = 2 and the cylinder x^2 + y^2 = 144.

Is the following statement always true? “If an irreducible Markov chain has period 2, then for every state i∈S we have P2ii>0.” (Prove if “yes”, provide a counterexample if “no”)

4. Consider a mixing tank with a volume of 50 gallons which is initially filled with 10 gallons of fresh water. Suppose there is an inflow pipe which pumps in a 1 lb/gallon brine (salt/water) mixture at a rate of 4 gallons per minute, and there is an outflow pipe which removes the mixture from the tank at a rate of 2 gallons per minute.

1. (a) Use the given information to derive an initial value problem which models the amount of salt in the tank as a function of time.

2. (b) Find the solution of the initial value problem.

3. (c) How much salt in the tank when the tank is full?

Create a program that calculate the amount of a mortgage payment. Refer to the appropriate video or any online source for how the mathematics of the calculation works. If given these three things:

• The amount of the loan in whole dollars
• The number of payments (e.g. 360 for 30-year)
• The interest rate per payment period in percent ( a positive floating-point number)

The program should print out the correct value (in dollars and cents) of the per-period payment of principal and interest (ignore escrow accounts, taxes, and insurance) for the following scenarios:

• 72 month loan of $20,000, 4.4% APR, compounded monthly
• 30 year loan of $150,000, 5% APR, one annual payment each year for 30 years

I am confused with the math behind finding the amount of a mortgage payment. Please explain the calculations behind the two above given scenarios.

Derive a formula for the volga of a European call option on a no-dividend underlying asset in the Black-Scholes model.

A body was found at 2pm in a room kept at 70 degrees. the student took the temp of the body and it was 80 degrees and then called the police 1 hour later the body was 75 degrees. Using newtons law of cooling determine the time of death. I know it is a Diff Q please show all steps. I will rate

Prove by strong mathematical induction that any integer greater than 1 is divisible by a prime number.

2.

a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2

b) Find a bound for the error in the interval [0, 1/2]

3. The following data is If all third order differences (not divided differences) are 2, determine the coefficient of x in P(x). prepared for a polynomial P of unknown degree P(x) 2 1 4

I need help with both. Thank you.

Show that the stereographic projection preserves the Euclidean angles

. A four-lane arterial (with two lanes in each direction) has a capacity of 1000 vehicleshourlane. Due to some road repair work, the maximum capacity of two lanes in the northbound direction is reduced to 1100 veh/hr from 2000 veh/hr for a short length of 200 ft. If the total traffic upstream of the repair site in the northbound lanes is reasonably at 1500 vehhr, find (a the mean speed of traffic through the repair site and (b) the stead rate at which the queue approaching the repair site grows. Assume the jam density is 200 vehicles/milenane.