Business Mathematics IIHomework 4Business Mathematics IIHomework 4Prepared forMath 174, PCC - NW Instructor: D’AlesandroDate: March 31, 2004ByTeam: We, the undersigned, maintain that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, orthe policies and procedures established for this course. ______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature______________________________ ______________________________Name (printed) Signature1. (Exercise 4 in Distributions) Consolidated Widget, Inc. has a force of 130 salespeople,whose sales performances can be considered to be independent of each other. The manager estimates that the probability of any one sales person reaching his or her monthly quota is 0.6. (i) What is the probability that at least 70 people make their quota?(ii) What is the probability that at most 70 people make their quota?Solution. 2. (Exercise 15 in Distributions) Use Integrating.xls to determine whether or not the function given below could be a p.d.f. for some continuous random variable.elsewhere010 if66)(2xxxxfXSolution. 3. (Exercise 16 in Distributions) Suppose that, on average, your company’s computer system goes down 10 times per week. Let T be the continuous random variable giving the time (in hours and fractions of hours) between system crashes. You are to use Excel to compute the probability that the time between computer system shutdowns will be between 15 and 30 hours. (i) Do this with the p.d.f., Xf. (ii) Do this with the c.d.f., XF.Solution. 4. (Exercise 20 Distributions) The sales department sends out instructional videotapes with your company’s product. When the tapes are produced, the recorder occasionally indicates that there is a single recording flaw in the tape at some unspecified point along its 700 foot length. On tapes with a single flaw, what is the probability that it occurs somewhere in the last 120 feet of the tape?Solution. 5. Let X be a continuous random variable that is uniform on the interval ]10,0[. (i) What is the probability that X is at most 8.75? (ii) What is the probability that X is no less than 4.25?Solution. 6. (Exercise 33 in Distributions) Use Excel and your team’s data for the signals on past oil leases to compute the complete set of errors in the signals. Find the sample mean of these errors and plot a histogram which approximates the actual p.d.f., Rf, of