The following data was recorded while observing the increase in the number of butterflies in two different ponds, Pond A and Pond B. Number of Butterflies Present Over 5 Years Year Pond A Pond B 0 50 1 2 3 4 5 100 110 121 133 146 161 65 85 110 143 186 What is the rate of growth, r, for each pond and which pond has the fastest average rate of growth over the five years?
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- Elon Corporation manufactures parts for an aircraft com-pany. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has adesign (nominal) target of 1.275 inches with tolerancesof 0.024 inch. The CNC process that manufacturesthese parts has a mean of 1.281 inches and a standarddeviation of 0.008 inch. Compute the process capabilityratio and process capability index, and comment onthe overall capability of the process to meet the designspecifications.Bill Kime's bowling ball factory makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.39 pounds. Each day for 24 days, the average weight, in pounds, of 9 of the bowling balls produced that day has been assessed as follows Day 1 2 3 4 5 6 Average (lb) 9.9 9.9 10.1 10.1 99 99 Day 7 8 9 10 11 12 Average (lb) Day Average (b) 13 14 15 16 17 18 10.1 10.0 10.0 10.1 10.1 10.0 9.9 10.1 10.1 10.0 10.1 10.1 Day 19 20 21 22 23 24 Average (lb) 99 10.0 10.1 9.9 10.0 10.0 a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean What are the values of the control limits? Upper Control Limit (UCL)=b (Round your response to two decimal places)Records pertaining to the monthly number of job-related injuries at an underground coal mine were being studied by a government agency. The values for the past 100 months were as follows: Injuries Frequency of per Month Occurrence 32 40 2 15 3 4 1. 1. Apply the chi-square test to these data to test the hypothesis that the underlying distribution is Poisson. Important note: In the answer box below, just put the numerical test statistic value. Use x.xx format for the numerical value you provide as the answer. Do NOT compare the test statistic with the critical value from a table. Answer:
- An industrial process that makes 3-foot sections of plasticpipe produces pipe with an average inside diameter of 1 inch and a standard deviation of .05 inch.a. If you randomly select one piece of pipe, what is the probability that its inside diameter willexceed 1.02 inches, assuming the population is normal?b. If you select a random sample of 25 pieces of pipe, what is the probability that the sample meanwill exceed 1.02 inches?μ = 1.00, σ = .05Mrs. Alaa works on developing staff training programs in Al Bustan Hotel to improve the services provided by the hotel She has been working their since 1990 and she mainly uses customers feedback on social media & customer complaints to forecast future training needs. The method used by Mrs. Alaa is a. Delphi b. Judgmental C Associative models d. Time seriesThe materials handling manager of a manufacturing company is trying to forecast the cost of maintenance for the company's fleet of over-the-road tractors. The manager believes that the cost of maintaining the tractors increases with their age. The following data was collected: Age (years) 5.5 where Y = Yearly maintenance cost in dollars and X = Age in years. 5.5 5.5 5.0 5.0 5.0 6.0 6.0 6.5 Yearly Maintenance Cost (S) 1,319 1,749 1,733 1,195 1,423 1,381 1,590 2,222 1,687 Age (years) 5.0 1.5 1.5 Y = 7.0 7.0 2.0 2.0 2.0 Yearly Maintenance Cost ($) 1,894 863 882 a. Use POM for Windows' least squares-linear regression module to develop a relationship to forecast the yearly maintenance cost based on the age of a tractor. (Enter your responses rounded to three decimal places and include a minus sign if necessary.) 1,464 2,073 1,678 1,166 1,249
- South Africa Airways would like to monitor its airline’s performance. Each week for the past 20 weeks, they checked each week a random sample of 100 flight arrivals for “one-time” performance. The table that follows contains the number of flights that did not meet South Africa Airways definition of “one time”: Week Late flights 1 2 2 4 3 10 4 4 5 1 6 1 7 13 8 9 9 11 10 0 11 3 12 4 13 2 14 2 15 8 16 2 17 3 18 7 19 3 20 2 Calculate the upper and lower control limits for this chart.A new fly spray is applied to 50 samples each of 5 flies and the number of living fliescounted after an hour. The results were as follows: Number living 0 1 2 3 4 5 frequency 7 20 12 9 1 1 i. Calculate the mean number of living flies per sample and hence an estimate for p, the probability of a fly surviving the sprayii. Using your estimate calculate the expected frequencies (each correct to one decimalplace) corresponding to a binomial distributioniii. Perform a chi – square goodness – of – fit test using a 5% significance level.(c)South Africa Airways would like to monitor its airline’s performance. Each week for the past 20 weeks, they checked each week a random sample of 100 flight arrivals for “one-time” performance. The table that follows contains the number of flights that did not meet South Africa Airways definition of “one time”: Week Late flights 1 2 2 4 3 10 4 4 5 1 6 1 7 13 8 9 9 11 10 0 11 3 12 4 13 2 14 2 15 8 16 2 17 3 18 7 19 3 20 2 Which control chart is appropriate to analyze the above data? Justify your answer
- A manufacturing company produces steel rods. The length of these rods is critical to their customers. The company aims to manufacture rods with a mean length of 150 cm. However, due to variability in the manufacturing process, the lengths of the rods follow a normal distribution. The company's quality control department samples 30 rods and finds that they have a mean length of 151 cm and a standard deviation of 2 cm. Calculate the Process Capability Index (Cp) and the Process Performance Index (Ppk) for this process. Assume the customer's specification limits are 147 cm and 153 cm for the length of the rods.An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: (4 year ago Quantity sold was 10842), (3 year ago Quantity sold was 11881 ), (2 year ago Quantity sold was 16064 ) and the last year Quantity sold was 19273 . The previous trend line had predicted 12250 for three years ago, 13000 for two years ago and 13750 for last year. What was the mean absolute percent error (MAPE) for these forecasts? a. 16.95 b. 2739 c. 0.17 d. 2985Bo Using data from 50 workers, a researcher estimates Wage = ẞe + B₁Education + B2Experience + B3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. Intercept Education Experience Age Coefficients Standard Error t Stat p-Value 7.17 4.26 1.68 0.0991 1.81 0.35 5.17 0.0000 0.45 0.10 4.50 0.0000 -0.01 0.06 -0.17 0.8684 a-1. Interpret the point estimate for ẞ1. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour, holding Age and Experience constant. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Experience constant. a-2. Interpret the point estimate for $2. As Experience…