A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as Poisson variate with mean 1.5. Calculate the proportion of days on which (i) neither car is used and (ii) some demand is refused,.
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- This question has 4 parts, Thank you.Suppose the number of off springs a female eagle raises during its lifetime has a distribution with mean 15 and variance 4. In an area, 45 rescued and cured female eagles are set free. If these eagles are assumed to be independent (no lack of male partners and food resources), the total number of off-springs produced by these eagles can be assumed to have a Normal distribution with mean and varianceLet wages denote hourly wages, educ years of education, and exper years of experience, and suppose log(wages) = f1 + 62educ + B3exper +e where E[eleduc, exper] = 0. Let b1, b2, and bz be our estimates for B1, B2, and ß3 and r23 denote the sample correlation between {educ,}", and {exper, }". Which of the following statements is true? II O a. The variance of b3 does not depend on r23. O b. The variance of b, is increasing in E" (educ, – educ,)² (all else equal). O c. The variance of b2 is at least as large as o²/ E", (educ, - educ,)2 for o? Var(eleduc, exper). O d. The variance of b2 depends on the sign of r23. O e. The variance of b2 always increases as r23 increases (all else equal).
- The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.86-0.45x. This line is shown in the scatter plot below. Mileage, x (in thousands) 29.7 27.8 26.8 24.2 21.1 23.0 24.3 15.4 37.7 23.6 34.4 27.8 23.5 20.9 259 Used selling price, y (in thousands of dollars) 27.4 29.4 31.2 30.1 31.7 31.7 27.2 34.2 23.4 28.2 26.3 26.5 33.7 30.6 267 Used selling price (in thousands of dollars) 40- 35+ 30- 25- 20 THIS 15 X 20 X X X 30 Mileagex (in thousands) X 35 40The frequency distribution table below is the net weight of a sample of candied fruit products in the food industry cans "ABC": - How many cans have a net weight of less than 20.2 grams. - If we want to compare about the distribution of net weight with the food company "XYZ" for the same type of product. And it is known that the average and variance is 20 grams and 0.04 grams. Which food company has an even distribution of net weight.The maximum weights (in kilograms) for which one repetition of a half squat can be performed and the times (in seconds) to run a 10-meter sprint for 12 international soccer players are shown in the attached data table with a sample correlation coefficient r of - 0.958. A 13th data point was added to the end of the data set for an international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 1.99 seconds. Describe how this affects the correlation coefficient r. Use technology. Click the icon to view the data set. Data Table The new correlation coefficient r going from - 0.958 to (Round to three decimal places as needed.) Maximum weight, x Time, y 175 1.81 185 1.79 155 2.06 210 1.42 155 2.07 195 1.62 190 1.69 165 1.88 195 1.59 180 1.64 165 1.97 175 1.91 210 1.99
- Calculate the Spearman correlation coefficient between two sets of data: set A = [6, 8, 10, 12, 14] and set B = [2, 4, 6, 8, 10].According to Zero Population Growth, the average urban U.S. resident consumes 3.3 pounds of food per day. Is this figure accurate for rural U.S. residents? Suppose 64 rural U.S. residents are identified by a random procedure and their average consumption per day is 3.60 pounds of food. Assume a population variance of 1.31 pounds of food per day. Use a 5% level of significance to determine whether the Zero Population Growth figure for urban U.S. residents also is true for rural U.S. residents on the basis of the sample data. Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.75.) The value of the test statistic is z = and weThe Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation Ŷ=42.80-0.53x. This line is shown in the scatter plot below. (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.)
- In a summary report given by Ing. Pobbi on the lengths of ironrods produced by two machines, he stated that the variability ofmachine A was higher compared to that of machine B. Critiquethe report of the Engineer given data on the length of rodsproduced given as; MachineA(cm): 380 410 280 310 305 360 270 355 400 Machine B(m): 1.1 1.3 1.2 2.0 1.5 1.6 1.4 1.6 1.7A process that cuts lengths of metal with high precision has historically produced metal rods with length that is normally distributed and with a mean of 800 millimetres (mm). Management at the factory is concerned that after an overhaul of the machine the mean length of the rods being produced could differ from the required 800 mm. If it is found that the rods are not being produced to specifications then the machine will have to be stopped for readjustment, with a consequent loss of production. The production line manager tasked with investigating the issue finds that a (random) sample of 25 rods yielded a mean length of 806 mm and a sample standard deviation of 10 mm. Use the Excel macro provided this session to test the hypotheses you have stated above using a 5% level of significance. You must show the Excel output and draw a conclusion from relevant values in the output.