Problem 4

For this week Problems activity, you will complete and submit the following items:

Chapter 6

· Problem 2 (Hint: Use the Countif function in Excel and the Binomial Probability Distribution Template)

· Problem 3 (Hint: Use the Poisson Probability Distribution Template)

· Problem 6 (Hint: Use the Inverse Normal Distribution Template and the Normal Distribution Template)

· Problem 10 (Hint: Use the Exponential Probability Distribution Template)

· Problem 20 (Hint: Use Descriptive Statistics tool in the Excel Data Analysis menu)

· Problem 21 (Hint: Use the single factor ANOVA tool in the Excel Data Analysis menu)

· Problem 24 (Hint: Use the 22 Factorial Experiment Template)

· Problem 25 (Hint: Use the 23 Factorial Experiment Template)

Note 1 : Many of the problems above will use the data sets found in C06Data.xlsx. In addition, the Excel Templates folder on the course home page contains 'templates' that will aid in solving many of these problems.

Note 2 : In order to earn credit for your answers to the problems, you are required to show all supporting work . Also, you may be expected to use Microsoft Office applications (Excel, Word, and/or PowerPoint) when showing your supporting work. If you use a 'template', save all of the information (numerical/visual).

Problem 2

2.

Auditors at the Valles Verdes Partners, P.S.C. took a sample of 150 accounts payable bills, as shown in the table found in the Excel worksheet Prob. 6-2 in the Excel workbook C06Data.xlsx.

a. Find the proportion of the accounts payable in the sample that are classified as overdue by using the Excel COUNTIF function.

b. If an auditor takes a random sample of only 15 accounts from this population, assuming that they follow a binomial distribution, what is the probability that: (i) exactly 6 bills will be overdue? (ii) 5 or fewer bills will be overdue? (iii) 7 or more bills will be overdue? Use the binomial probability distribution formula and verify your result using Excel Binomial spread-

sheet template

PROBLEM 3

3.

The Turkalike Rug Company buys medium grade

carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution, use the Poisson spreadsheet template to answer the following questions.

a. What is the probability of finding exactly 6 defects in a carpet roll chosen at random?

b. What is the probability of finding 3 or fewer defects in a carpet roll?

PROBLEM 6

6.

Frackly Oil is sold in 900 milliliter (ml) cans. The mean volume of oil placed in a can is 880 ml with a standard deviation of 7.8 ml. Assuming a normal distribution of the data, what is the probability that the filling machine will cause an overflow in a can, that is, the probability that more than 900 ml will be placed in the can?

PROBLEM 10

Genjeteye, Inc. makes aircraft engines. The mean time to failure has been found to be 100,000 hours and is exponentially distributed.

a. What is the failure rate, λ, per hour?

b. What is the cumulative probability of failure after 10,000 hours or fewer? Between 10,000 and 15,000 hours?

c. If Genjeteye wishes to provide a warranty that no more than 5 percent of the units will fail, how many hours of operation without failure should the company guarantee?

Problem 20

20.

Rabbitfoot Community Bank makes a large num- ber of home equity loans each year. The vice pres- ident of loan administration wishes to determine if their time for paperwork processing is lower than the average time of their top competitor. A sample of 30 loans taken at Rabbitfoot Bank yielded a mean of 38.10 minutes and a standard deviation of 2.58 minutes (see the data in the Ch06Data Excel workbook). Data obtained from competitor of 36 applications indicates that the average time for processing an application is 39.48 minutes, with a standard deviation of 2.48 minutes.

Problem 21

Softswell, a software developer, is trying to deter- mine if any of three potential subcontractors has better programmers in order to outsource a devel- opment project. The three subcontractors agreed to test 5 programmers, using a standardized test provided by Softswell, as provided in the data in the Ch06Data Excel workbook. Use the single fac- tor ANOVA Excel tool to determine if there is a significant difference between the scores of pro- grammers at the three contractors at the 5 percent level.

Problem 24

A quality analyst at Paintfast Manufacturing Co. wants to determine if a new paint formulation, used to paint parts for a customer’s assembly oper- ation will dry fast enough to meet the customer’s needs. The customer would prefer to obtain a high level of “dryability” at low temperatures, even if it requires a higher level of drying agent. He hypothesizes that a high level of drying agent will result in high dryability, high temperature— alone—will result in a moderately high level of dryability, and low temperature or a low level of drying agent will result in a low level of dryability. He hopes that the main and interaction effects with the temperature, which is expensive (because an oven would need to be used), will be minimal. The data found in the worksheet Prob. 6-24 in the Excel workbook C06Data were gathered in testing all combinations. What recommendation would you make?

Problem 25

The process engineer at Sival Electronics is also trying to determine whether a newer, more costly design involving a gold alloy in a computer chip is more effective than the present, less expensive sili- con design. She wants to obtain an effective output voltage at both high and low temperatures, when tested with high and low signal strength. She hypothesizes that high signal strength will result in higher voltage output, low temperature will result in higher output, and the gold alloy will

1. Devise an experiment similar to the battery per- formance test case (see the Battery Experiment case that follows) to test different levels of some factor and conduct a statistical analysis of the results. Write up your experiment and results in a report along with the conclusions that you reach from the analysis. You might wish to con- sult the following paper: “101 Ways to Design an Experiment, or Some Ideas About Teaching Design of Experiments” by William G. Hunter, Technical Report No. 413 dated June 1975 at

SIZZLEKING BURRITO HOUSE

result in higher output than the silicon material. She hopes that the main and interaction effects with the expensive gold will be minimal. The data found in the worksheet Prob. 6-25 in the Excel workbook C06Data were gathered in testing of all combinations. What recommendation would you make?