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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- You are a food specialist in a company that specializes inrefrigerated delicacies, and one of your brands requires beingmaintained at a temperature of 5°C. You determine averagewater activity (aw) at this temperature to be 0.2. One day, you are informed that the cooling systems onone of the delivery trucks carrying your company’s productsmalfunctioned while en route to its destination and it would notbe fixed until the next delivery. The driver has informed you thatthe temperature in the delivery bay of the truck is averaging55°C. You estimate a heat of sorption (Q) of 19 kJ/mol. Calculate the water activity of the brand at this elevatedtemperature and comment on it’s integrity. Should the deliverystill push through? Or should the products be recalled anddisposedGiven the attached data. Answer the following questions for a 7 period moving average. t At 1 5477 2 3338 3 4799 4 2852 5 6332 6 8385 7 4382 8 4184 9 14229 10 10385 11 11676 12 5271 13 8938 14 9279 15 13990 16 2890 17 13027 18 8970 19 6700 20 7065 21 12491 22 8748 23 8396 24 6102 25 7559 26 7997 27 11981 28 10680 29 5783 30 2501 31 7620 32 10194 33 7908 34 11985 35 5863 36 3024 37 8758 38 1640 39 6569 40 11728 41 6659 42 2830 43 10018 44 8448 45 12409 46 2083 47 6374 48 7438 49 4576 50 4795 MAD = Average(|A-F|) TS =SUM(A-F)/MAD MSE = Average(A-F)2 1. Compute your forecast for period 51. The potential answers are: A: 11221.6 units. B: 12461 units. C: 8020.83 units. D: 4414 units. E: 6589 units.Explain or define each of these terms:a. Laplace criterionb. Minimax regretc. Expected valued. Expected value of perfect information
- A well-known multinational FMCG produces more than fifty products and sells them in the market. Out of fifty products one is mineral water for drinking purpose and supplies different size pack bottles in the market. Product manager observed that, during hot days the sale of water is more as compared to the normal days. He started the collection of data of weekly sale of water and the average weekly temperature. Product manager was interested in developing a relationship between sales and temperature; therefore, he discussed and shared the following data with youElon 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.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)
- 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 = .05Which one of the following methods eliminates short term and random fluctuations in a time series? a. Moving Average b. Semi-Average c. Neither moving average nor semi average d. Both moving average and semi-averageThe director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529. State the null and alternative hypotheses for the above scenario.
- As employees leave a company, they are asked to rate their level of job satisfaction during the time they were employed by the company. A sample set of scores (out of a maximum of 10) is provided below. 3 6 4 4 5 2 1 3 2 5 3 7 2 2 3 1 9 1 Use the information provided in the table to calculate: The median; The mode; The mean; The lower quartile (Q1); The upper quartile (Q3); The interquartile range (IQR); The standard deviation. State whether or not the ex-employees were likely to have left the company as a result of lack of job satisfaction. Use the statistics above to justify your conclusion. Discuss in which ways the company could benefit from making these statistics available to its current employees.Prior to conducting double exponential smoothing a simple linear regression is conducted and the trend equation is Y=42+38.3t, so the smoothed constant process value should be C0=38.3 and the smoothed trend value should be T0=42.? TRUE OR FALSE?The Scottsdale fire department aims to respond to fire calls in 7 minutes or less, on average. Response times are normally distributed with a standard deviation of 1 minute 42 seconds. Would a sample of 18 fire calls with a mean response time of 7 minutes 21 seconds provide sufficient evidence to show that the goal is not being met at α = .01?