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Math 533 week 8 final exam – three different set

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**MATH 533 Week 8 Final Exam – Three Different Set**

**MATH 533 Applied Managerial Statistics – DeVry**

** **

**Set 1**

**1. (TCO D)** PuttingPeople2Work has a growing business placing out-of-work MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample.

– Sample size: 100 – Population standard deviation: 5 – Sample mean: 34.2 – Formulate a hypothesis test to evaluate the claim. (Points : 10)

**2. (TCO B)** The Republican party is interested in studying the number of republicans that might vote in a particular congressional district. Assume that the number of voters is binomially distributed by party affiliation (either republican or not republican). If 10 people show up at the polls, determine the following: Binomial distribution………What is the probability that no more than four will be republicans? (Points : 10)

**3. (TCO A)** Company ABC had sales per month as listed below. Using the Minitab output given, determine:

(A) Range (5 points) (B) Median (5 points) and (C) The range of the data that would contain 68% of the results. (5 points).

**4. (TCO C, D)** Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla’s requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer. Descriptive statistics……..

**5. (TCO D)** A PC manufacturer claims that no more than 2% of their machines are defective. In a random sample of 100 machines, it is found that 4.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacturer’s claim, and explain your answer.

**6. (TCO B)** The following table gives the number of visits to recreational facilities by kind and geographical region. (Points : 30) **(A)** Referring to the above table, if a visitor is chosen at random, what is the probability that he or she is either from the South or from the West? (15 points) **(B)** Referring to the above table, given that the visitor is from the Midwest, what is the probability that he or she visited a local park? (15 points)

**7. (TCO B, F)** The length of time Americans exercise each week is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes **(A)** Analyze the output above to determine what percentage of Americans will exercise between 11 and 21 minutes per week. (15 points) **(B)** What percentage of Americans will exercise less than 15 minutes? If 1000 Americans were evaluated, how many would you expect to have exercised less than 15 minutes? (15 points) (Points : 30)

**Set 2**

**1. ****(TCO A)** Seventeen salespeople reported the following number of sales calls completed last month.

**2. ****(TCO B)** Cedar Home Furnishings has collected data on their customers in terms of whether they reside in an urban location or a suburban location, as well as rating the customers as either “good,” “borderline,” or “poor.” The data is below

**3. ****(TCO B)** Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that

**4. ****(TCO B)** The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day

**5. ****(TCO C)** An operations analyst from an airline company has been asked to develop a fairly accurate estimate of the mean refueling and baggage handling time at a foreign airport. A random sample of 36 refueling and baggage handling times yields the following results

**6. ****(TCO C)** The manufacturer of a certain brand of toothpaste claims that a high percentage of dentists recommend the use of their toothpaste. A random sample of 400 dentists results in 310 recommending their toothpaste.

**7. ****(TCO D)** A Ford Motor Company quality improvement team believes that its recently implemented defect reduction program has reduced the proportion of paint defects. Prior to the implementation of the program, the proportion of paint defects was .03 and had been stationary for the past 6 months. Ford selects a random sample of 2,000 cars built after the implementation of the defect reduction program. There were 45 cars with paint defects in that sample. Does the sample data provide evidence to conclude that the proportion of paint defects is now less than .03 (with a= .01)? Use the hypothesis testing procedure outlined below.

**8. ****(TCO D)** A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars gives the following result.

**9. ****(TCO E)** Bill McFarland is a real estate broker who specializes in selling farmland in a large western state. Because Bill advises many of his clients about pricing their land, he is interested in developing a pricing formula of some type. He feels he could increase his business significantly if he could accurately determine the value of a farmer’s land. A geologist tells Bill that the soil and rock characteristics in most of the area that Bill sells do not vary much. Thus the price of land should depend greatly on acreage. Bill selects a sample of 30 plots recently sold. The data is found below (in Minitab), **where X=Acreage and Y=Price ($1,000s)**.

**10. ****(TCO E)** An insurance firm wishes to study the relationship between driving experience (X1, in years), number of driving violations in the past three years (X2), and current monthly auto insurance premium (Y). A sample of 12 insured drivers is selected at random. The data is given below (in MINITAB):

**Set 3**

**1. **The length of time to do a cable installation by Multi-Cable Inc. is normally distributed with a mean of 42.8 minutes and a standard deviation of 6.2 minutes. What percentage of installations take less than 30 minutes?

**2.** Accident claims are checked for completeness by branch offices of Fortune Insurance before they are sent to a regional office for payment. Historically 80% of the claims are complete when they reach the regional office. You select a random sample of 20 claims that have arrived at the regional office. Find the probability that:

**3.** Until this year the mean braking distance of a Nikton automobile moving at 60 miles per hour was 175 feet. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 81 cars and determine the sample mean braking distance. The results are:

**4.**The manager at Trion Electric Co-op is concerned about the rise in the number of late payments. If more than 10% of the accounts are behind in their payments, the manager will initiate a costly monitoring program. A random sample of 75 accounts shows that 9 were behind in their payments.

**5.** A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 pairs of shoes leads to the following results in terms of useful life:

**6.** AJ AUCTION sells art drawings of little known artist at auction. The dealer is interested in the relationship between the final sale price ($) (Y) and the number of persons bidding on the drawing (X). A random sample of 20 drawing is selected.

**7.** The personnel department of a large industrial corporation would like to develop a model to predict the weekly salary based upon the length of employment and age of its managerial employees. Salary is modeled as a linear function of length of employment and age.

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