Business Mathematics IHomework 9Business Mathematics IHomework 9Prepared forLotfi Hermi Math 115a, Section 004University of Arizona ByTeam #Submitted onDecember 5, 2005We, the undersigned, affirm that all of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we understand that sanctions will be imposed individually as well as jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) Signature______________________________ ______________________________Name (typed) SignatureExercise 1 Go to Excel and use RAND to create a column of 12 random numbers, between 0 and1. Take a screen shot of your experiment.Exercise 2 Add a column to the file If.xls that simulates 10 tosses of a coin that is loaded in sucha way that 3.0)( TP. Show the formula that you used in the column. Make sure to record a screen shot of this simulation below.Exercise 3 Add a column to the file If.xls that simulates 10 tosses of a coin that is loaded in sucha way that you are three times as likely to get a tail as a head. Show the formula that you used inthe column.Exercise 4 Open the file Coins.xls and note how IF and RANDBETWEEN are used to simulate coin tosses. (i) Modify this method to create an Excel file that simulates 20 tosses of a fair die. (Take screen shots of your observations and copy them below). (ii) Explain why this method would be very difficult to use in the simulation of coin tosses for a biased coin with4039.0)( TP.Exercise 5 Consider the experiment of tossing a fair coin three times, and let X be the number of heads that occur in such a set of tosses. Use Excel to simulate 2,000 observations of X and then use these to estimate )(XE and)1( XP.Exercise 6 Modify the Excel file Queuing Example 2.xls, so that it will create, and correctly plot, random samples of size 500 for an exponential random variable, X, with parameter 10. Your answer should contain the frequency histogram, as well as the p.d.f.’s for the sample and the exponential function fit. Be careful how you choose the bin width. Focus on the Project**Exercise 7** Create new worksheets or modify the worksheets in Queue Focus.xls to accommodate the maximum number of arrivals that is indicated in your team assignment. Note that the allowable maximum number of arrivals in worksheets of Queue Focus.xls cannot be extended by simply dragging down existing rows. For example, the entries in Column L of 1 ATM depend on criteria ranges that contain two rows. After these cells are dragged down, they will need to be adjusted with individual typing. The necessary extensions of criteria ranges will also require careful thought. In addition, you will need to adjust the ranges of rows that are considered in all summary cells as well as the Overflow cutoffs. **Exercise 8** Modify your team data worksheets so that all simulations kept track of the numbers of customers who are irritated.**Exercise 8** (i) Collect summary data from at least 2,000 simulations for each of 1 ATM, 2 ATM’s, 3 ATM’s, and 3 ATM’s with serpentine queue during your team’s first hour. (ii) Repeat Part (i) for your team’s second hour. **Exercise 9** (i) Create tables, similar to those in the Focus on the Project Section, that display the numbers of ATM’s and (in the case of 3 ATM’s) the type of queues that would be needed to validate each of your team’s possible advertising claims during your team’s first hour (9 AM). (ii) Repeat Part (i) for your second hour (9
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