Scenario

Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem.

Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer’s office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour.

OEI is planning to expand its business. Within 1 year, OEI projects that it will have 20 customers, and within 2 years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average 3-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when OEI reaches 20 customers and to add a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average 3-hour waiting time guarantee at the lowest possible total cost.

Managerial Report

Develop a managerial report (1,000-1,250 words) summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 and then 30 customers, and justify your response. Include a discussion of the following issues in your report:

1. What is the arrival rate for each customer?
2. What is the service rate in terms of the number of customers per hour? (Remember that the average travel time of 1 hour is counted as service time because the time that the service technician is busy handling a service call includes the travel time in addition to the time required to complete the repair.)
3. Waiting line models generally assume that the arriving customers are in the same location as the service facility. Consider how OEI is different in this regard, given that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time? Explain.
4. OEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information: (a) probability that no customers are in the system, (b) average number of customers in the waiting line, (c) average number of customers in the system, (d) average time a customer waits until the service technician arrives, (e) average time a customer waits until the machine is back in operation, (f) probability that a customer will have to wait more than one hour for the service technician to arrive, and (g) the total cost per hour for the service operation.
5. Do you agree with OEI management that one technician can meet the average 3-hour service call guarantee? Why or why not?
6. What is your recommendation for the number of service technicians to hire when OEI expands to 20 customers? Use the information that you developed in Question 4 (above) to justify your answer.
7. What is your recommendation for the number of service technicians to hire when OEI expands to 30 customers? Use the information that you developed in Question 4 (above) to justify your answer.
8. What are the annual savings of your recommendation in Question 6 (above) compared to the planning committee's proposal that 30 customers will require three service technicians? (Assume 250 days of operation per year.) How was this determination reached?

Please provide a new answer old ones where incorrect.

• Suppose reaction time for drag racers is know to be on average 50 ms with a standard deviation of 10 ms and that reaction time is normally distributed.

1. • What is the reaction time that separates the fastest 10% of racers from the rest?
2. What is the interval that contains the middle 95% of racers?
3. Above what value would you expect to find the slowest 60%?

Can you please explain in detail? plus i know for this problem we have to use this formula X= z x standard deviation + mean. Where do i get the z for this problem? i know the mean and Standard deviation but where am i supposed to get the Z?

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 30 0 20 12 19 18 23 −22 −24 −21 y: 11 −5 9 8 21 25 22 −3 −7 −2 (a) Compute Σx, Σx2, Σy, Σy2. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) x y x s2 s (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) x y Lower Limit Upper Limit Use the intervals to compare the two funds. 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 25% of the returns for the stock fund fall within a wider range than those of the balanced fund. (d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.) x y CV % % Use the coefficients of variation to compare the two funds. For each unit of return, the stock fund has lower risk. For each unit of return, the balanced fund has lower risk. For each unit of return, the funds have equal risk. If s represents risks and x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. A smaller CV is better because it indicates a higher risk per unit of expected return. A smaller CV is better because it indicates a lower risk per unit of expected return.

Suppose there is a normally distributed population which has a mean of μ = 440and a standard deviation of σ = 60. (15p)

1.What portion of a normal distribution is below 295?

2. What z-score would correspond to a raw score of 260?

3. What raw score would correspond to a z score of -3.5?

4. If we randomly select one score from this population, what is the probability that will be less than 550?

5. If we randomly select one score from this population, what is the probability that will be greater than 580?

"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

(a) Find the mean, median, and mode. (Round your answers to two decimal places.)

(b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)

(c) Based on the data, would you recommend radon mitigation in this house? Explain.

Yes, since the median value is over "acceptable" ranges, although the mean value is not.Yes, since the average and median values are both over "acceptable" ranges.    No, since the average and median values are both under "acceptable" ranges.Yes, since the average value is over "acceptable" ranges, although the median value is not.

Respond to all of the following questions in your posting for this week:

• Describe the characteristics of the F distribution. Provide examples.
• What are we testing when we test for two population variances? Explain your answer and provide an example.
• What are the assumptions of an ANOVA, and when would you use an ANOVA?

Suppose certain coins have weights that are normally distributed with a mean of

5.641 g5.641 g

and a standard deviation of

0.069 g0.069 g.

A vending machine is configured to accept those coins with weights between

5.5215.521

g and

5.7615.761

g.

a. If

300300

different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?The expected number of rejected coins is

2525.

​(Round to the nearest​ integer.)b. If

300300

different coins are inserted into the vending​ machine, what is the probability that the mean falls between the limits of

5.5215.521

g and

5.7615.761

​g?The probability is approximately

(missing data)

​(Round to four decimal places as​ needed.)

In models for the lifetimes of mechanical components, one sometimes uses random variables with distribution functions from the so-called Weibull family. Here is an example: F(x) = 0 for x < 0, and F(x) = 1 − e^{−5x^2} for x ≥ 0.
Construct a random variable Z with this distribution from a U(0, 1) variable.

Use Excel to perform the calculations and attach it/screenshot it

A researcher compares the effectiveness of two different instructional methods for teaching electronics. A sample of 138 students using Method 1 produces a testing average of 61 . A sample of 156 students using Method 2 produces a testing average of 64.6 . Assume that the population standard deviation for Method 1 is 18.53 , while the population standard deviation for Method 2 is 13.43 . Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

An urn contains 10 red and 12 blue balls. They are withdrawn one at a time without replacement until a total of 4 red balls have been withdrawn. Find the probability that exactly 7 balls withdrawn/

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twenty-six 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

1The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. 2The probability in part (b) is much higher because the mean is larger for the x distribution. 3The probability in part (b) is much lower because the standard deviation is smaller for the x distribution. 4The probability in part (b) is much higher because the standard deviation is larger for the x distribution.5The probability in part (b) is much higher because the mean is smaller for the x distribution.

PLease show work in excell

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

A listing of the jobs by title

The salary (in dollars) for each job

The client needs the preliminary findings by the end of the day, and your boss asks you to first compute some basic statistics.

Background information on the Data

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several j

obs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

What to Submit

Your boss wants you to submit the spreadsheet with the completed calculations. Your research and analysis should be present within the answers provided on the worksheet.

Income East and West of the Mississippi

For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether there is a difference in average household income between those east of the Mississippi and those west of the Mississippi.

Incorrect answer iconYour answer is incorrect.

(a) State the null and alternative hypotheses. Your answer should be an expression composed of symbols:

Let group 1 be the households east of the Mississippi River and let group 2 be the households west of the Mississippi River.

(b) What statistic(s) from the sample would we use to estimate the difference?

Let group 1 be the households east of the Mississippi River and let group 2 be the households west of the Mississippi River.

The output voltage of a power supply unit has an unknown distribution. Using a sample size of 36, sixteen samples are taken with the following sample-mean values: 10.35 V, 9.30 V, 10.00 V, 9.96 V, 11.65 V, 12.00 V, 11.25 V, 9.58 V, 11.54 V, 9.95 V, 10.28 V, 8.37 V, 10.44 V, 9.25 V 9.38 V and 10.85 V. Let µ and σ² denote the mean and the variance of the output voltage of the power supply unit. (a) What distribution describes the sample-mean? What are the parameters of the distribution (in terms of µ and σ² )? (b) Test the hypothesis that the population variance σ² = 36 V² at 95% confidence. (c) Construct a two-sided 95% confidence interval for the population’s standard deviation.