Business Mathematics IIHomework 9Business Mathematics IIHomework 9Prepared forMath 115b, Section: Instructor: Date: ByTeam: 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. (i) Use Random Number Generation to generate a random sample of size 1000 from anormal random variable, X, with 145X and 20X. (ii) Use the sample to computean estimate of )90( XP. (iii) Use NORMDIST to compute )90( XP. (iv) How do the values from Parts (ii) and (iii) compare?Solution. 2. (i) Use Random Number Generation to generate a random sample of size 500 from a normal random variable, X, with 110X and 15X. (ii) Use the sample to computean estimate of )125( XP. (iii) Use NORMDIST to compute )125( XP. (iv) How do the values from Parts (ii) and (iii) compare?Solution. 3. (i) Use Random Number Generation to generate a random sample of size 2000 from anormal random variable, X, with 85X and 10X. (ii) Use the sample to compute an estimate of )60( XP. (iii) Use NORMDIST to compute )60( XP. (iv) How do the values from Parts (ii) and (iii) compare?Solution. 4. (Exercise 13 in Simulating Normal Random Variables) Modify the sheet Intervals in Salary.xls so that it computes the end points of 90% confidence intervals for the mean ofX. What fraction of these intervals actually contain $88,989?Solution. 5. Let X be a normal random variable with mean 140X and 15X, and let Y be a normal random variable with mean 140Y and 25Y. (i) Use Random Number Generation to generate a random sample of size 1000 from X and to generate a random sample of size 1000 from Y. (ii) Have Excel compute a 95% confidence interval from each sample. (iii) How does the confidence interval for X compare with the confidence interval for Y?Solution. 6. Let X be a normal random variable with mean 115X and 20X, and let Y be a normal random variable with mean 115Y and 10Y. (i) Use Random Number Generation to generate a random sample of size 500 from X and to generate a random sample of size 500 from Y. (ii) Have Excel compute a 95% confidence interval from eachsample. (iii) How does the confidence interval for X compare with the confidence interval for