Mathematics for Business Decisions, Part IIHomework 9Mathematics for Business Decisions, Part IIHomework 9forMath 115b, Section: Instructor: James BarrettDate: 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, or the policies and procedures established for this course. _ Name Typed Signature % of Grade__________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ ______________________________ _____________________________ _______________________________ _____________________________ ____________1. (i) Suppose that the county administrator in Text Example 3 had planned to take a random sample of size n=100. (i) If the sample mean and standard deviation of $88,989 and $22,358had come from a sample of 100 administrators, compute the 95% confidence interval for μX. (ii) With the larger sample size, could the administrator claim, at the 95% level, that his salary is below the national average? Show all work..Solution:2. In a previous exercise, you found a number z1 such that P(Z≤ z1)=0. 9500. Use this to modify our computations and find a 90% confidence interval for the mean of county administrators’ salaries. Use the 50 samples that our administrator took to compute the 90% confidence interval. Can he claim that, at the 90% level, his salary is below the national mean?Solution. 3. Let Y be a normal random variable with a mean of $1,374,505 and a standard deviation of $98,751. Use Integrating.xlsm to compute P($ 1 , 300 , 000≤Y ≤$ 1 , 500 , 000) and to display a graph of fY. Show table from Integrating.xlsm.Solution. 4. Let Y be as in problem 3 above. Use Integrating.xlsm to compute P($ 1 , 400 ,000≤Y ). Show table.Solution. 5. Let T be a normal random variable with a mean of 8 days, 12 hours and a standard deviation of 1 day, 5 hours. Use Integrating.xlsm to compute P(7 days≤T≤10 days ) and to display a graph of fT. Show table.Solution.6. Let T be as in problem 5 above. Use Integrating.xlsm to compute P(T ≤6 ) days. Show table.Solution. 7. A random sample from a normal random variable, Y, is listed in the Excel file Exercise Data.xls. Use this data to estimate the parameters of Y and then useNORMDIST to compute P($ 98 ,000≤Y ).Solution. 8. The replacement time, T, of a new television set is a normal random variable withμT=8. 2 years and σT=1. 1 years. Compute the probability that the replacement time of anew television set will be less than 6 years.Solution:9. The amount of coffee that a vending machine dispenses into 6-ounce cups is a normal random variable with a mean of 5.4 ounces and a standard deviation of 0.3 ounce. Compute the probability the vending machine will overfill a cup.Solution. 10. Let X be a normal random variable with a mean of $120,000 and a standard deviation of $18,000. (i) Use NORMDIST and Graphing.xlsm to plot the p.d.f., fX( x ). (ii) Use NORMDIST and Graphing.xlsm to plot the c.d.f., FX( x ).Solution.11.. Let X be an exponential random variable with parameter α=5. (i) Use Graphing.xlsm to plot the p.d.f., fX, over the interval [0, 40 ]. (ii) Use Differentiating.xlsm to plot the derivative of the c.d.f., FX, over the same interval. (iii) How do the plots from Parts (i) and (ii) compare?Solution. 12. Use the estimated parameters for your team’s error data to create a histogram and smooth graph that approximate both the estimated and normal probability density functions for R. This will be similar to the work on the Class Project in the sheet Normal of Auction Focus.xlsx. Does your random variable, R, have a normal distribution? Let C and B be random variables for your team’s data which are analogous to those for the Class Project, as described in the Focus pages of this section. Use your team’s data and normal simulation to estimate E(C) and
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