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atulsingh03proDeendayal Upadhyaya Gorakhpur University

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I am Atul Kumar Singh from Uttar Pradesh, India. Currently I am pursuing CA (Chartered Accountancy) Course and B. COM (Bachelor of Commerce) from Deen Dayal Upadhyaya Universit...

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Architecture1Project Management4History9Law1Management3English12Philosophy5Business10Marketing6Science4Mechanical Engineering1Sociology2Ethics2Information Technology7Algebra24Engineering2Geometry1Computer Science24Accounting162Calculus8Biology66Mathematics1Statistics1452Physics4Finance556Economics163Chemistry31
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Pe Chapter 6, Problem 12RE 2 Bookmarks Show all steps: ON Problem Consult Table 5.1, the 1992 abridged lite table for the United States (1) (a) What is the probability that a newborn infant will live to see his or her with birthday? (b) What is the probability that an individual who is 60 years old will survive for the next ten years? (c) Consider a man and woman who are married and who are both 60 years of age. What is the probability that both the woman and her husband will be alive on their 70th birthdays? Assume that the tivo events are independent (d) What is the probability that either the wife or the husband, but not both, will be alive at age 70? Step-by-step solution Step 1 of 4 A Refer to the 1992 abridged life table for United States. The probability that a newbom wil Ive to see his or her fifth birthday is, 0.00851 0.00172 = 0.01023 The required answer is 0.01023 Comments (2) Anonymous This is incorrect Anonymous I agree, this is wrong, the right answer is 0.98978 Submit 98 Chapter 5 Life Tobles TABLE 5.7 Abridged life table for the total population, United States, 1992 Stationary Population Of 100.000 Born Alive Age Interval Proportion Dying Yea Re Period of Life between Two Exact Ages Stated in Years (1) Proportion of Persons Alive at Beginning of Age Interval Dying during Interval (2) Number Living at Beginning of Age Interval (3) Number Dying during Age Interval In the Age Interval (5) In This and Alt Subsequent Age Intervals (6) torta 851 171 66.6 99,275 396,195 494,615 494,152 492.848 490,448 487.654 484,369 0-1 1-5 ....... 5-10 ...... 10--15 ... 15-20 ...... 20-25 ..... 25-30 ..... 30-35 ...... 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 ... 75-80 ..... 80-85 ..... 85 and over .. 480.187 0.00851 0.00172 0.00102 0.00121 0.00418 0.00528 0.00601 0.00765 0.01001 0.01305 0.01822 0.02799 0.04421 0.06800 0.10084 0.14673 0.21189 0.31480 1.00000 101 120 413 519 588 744 966 1247 1718 2591 3978 100.000 99.149 98.978 98.877 98,757 98.344 97.825 97,237 96,493 95.527 94.280 92,562 89.971 85.993 80,145 72,063 61,489 48,460 33,205 7.577.757 7,478,482 7,082.287 6,587,672 6,093.520 5.600,672 5.110.224 4,622,570 4.138.201 3,658,014 3.183.274 2.715,854 2.259,115 1.818,634 1.402.497 1,021,104 686,305 410,638 474,740 467,420 456,739 440,481 416,137 381,393 334.799 275,667 204,369 5848 8082 10.574 13.029 15,255 33,205 85 206,269 206,269 length of the interval. Therefore, 0-1 designates the one-year period of life fre until an individual's first birthday. Interval 1-5 represents the time from the fir day until the fifth birthday, a period of four years. All other age intervals span fr except for the last. This is an open-ended interval representing the entire peri beyond the 85th birthday. For the sake of convenience, abridged life tables-such as Table 5.1 most often in practice. Abridged tables display data in terms of five-year ag A complete life table would have an entry for each year, the complete lif culated for the U.S. population in 1979-1981 is shown in Table 5.8, at the chapter 13). In the United States, complete life tables are constructed eve
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M ANE 4352 - Manufacturing Simulation Homework No. 2 Spring 2020 Posted: Saturday, January 25, 2020 Due: Friday, February 7, 2020 Solution Posted: Monday, February 10, 2020, 11:59 pm Please work the following problems. Please show all of the steps in the determination of the solution. The point value of each problem is shown in the brackets behind the problem number 1.[25] Coefficient of restitution for a golf ball hitting the head of a golf club is an important parameter for golf club performance. (A higher value means more energy restored to the ball in flight, and therefore, a better drive with the golf club.) Restitution coefficients are measured for golf club X brand, with the following values given in Table 1. The golf club manufacturer states that the restitution meets or exceeds 0.82. Perform a test of hypothesis with a = 5%. Table 1 - Golf Club Brand X Coefficient of Restitution Experiment 0.8411 0.8582 0.8042 0.8191 0.8532 0.8730 0.8182 0.8483 0.8282 0.8125 0.8276 0.8359 0.8750 0.7983 0.8660 2. [25] A new manufacturing process is believed to have surface defects which follow a Poisson Distribution. The surface defects found in a sample of 30 sheets is contained in Table 2, below. Estimate the mean for this poisson Distribution and use a Chi Squared Goodness of Fit test to prove that Poisson is or is not a good fit. Table 2 - Poisson Distribution Data Number Found 03 6 2 3 4 6 or more 3. [25] Develop a LCG random number generator in a spreadsheet for the following constants: Z = 17, a = 31, c= 5, and m = 73. Generate 72 random numbers. Change the value of a to 23 and describe what happens. 4. [25] The data in Table 3, below is believed to come from an exponential distribution with a mean of 3. Use Kolmogrov-Smirnov procedures to prove or disprove this hypothesis at the a = 0.05% level. Table 3 - Data for Analysis with Kolmogrov-Smirnov 3 0.1 2.9 4.2 2.4 2.7 2.0 10 od 600 V 3.4 2.1 0.4 13 0.2 1.4 2.2 14 3.1 15 4.1 16 1.2 174.1 18 191.3 200.7 3.6
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Meeting Demands in a Fitness Center Individuals who become members of a fitness center do sọ for a variety of reasons, but one reason is often the availability of specialized facilities or equipment. Consequently, man- agement of the center is sensitive to the need for meeting member demand for equipment. At the same time, providing specific equipment requires funds to purchase and maintain it and space to house it. Indeed, because of financial and space constraints, making a decision to purchase a specific piece of equipment may mean that other equipment cannot be purchased. We consider a situation where management of a fitness center is evaluating whether it has enough stationary bicycles to meet the demand. There are currently five bicycles, and the demand in the early morning appears to exceed the capacity. Management believes members are frustated by the need to wait for bicycles in the period from 6:00 a.m. to 7:30 a.m.., add more bicycles. Data have been collected on equipment utilization between 6:00 a.m. and 7:30 a.m., and the data include arrival times and excercise times. The data represent observations of a stochastic process (actually several stochastic processes), and to simplify the modeling process, it is helpful to make assumptions about the underlying distributions for these random variables. Suppose that data are collected and reviewed with a goal of making reasonably simple assumptions about arrival rates. On the basis of the review, we assume that the rate of arrivals in the period 6:00 to 7:30 a.m. varies, with a peak arrival rate during the 30-minule period from 6:30 to 7:00 and lower rates before 6:30 and after 7:00. More specifically, we assume that arrivals have an exponential distribution with an average of 30 arrivals in the period from 6:00 to 6:30, an average of 45 arrivals in the period from 6:30 to 7:00, and an average of 20 arrivals in the period from 7:00 to 7:30, and the goal of the study is to determine whether it is economically desirable to Suppose that most of the members use the bicycles as part of an exercise program Let includes other activities, and we assume that the period of excercise time spent on the eycles is of fixed duration for all members: 8 minutes. Finally, we assume that if no bicycle DIe ailable when a member arrives, the member will wait for one to become available if IS e are three or fewer members waiting, but if there are four members already waiting, then the new arrival will leave. With these assumptions, we can simulate a single day as follows: We consider each ute of the 90-minute period, one minute after another, and we determine whether one amore of the members currently using a bike completes a session during that minute. If cach of the bicycles released becomes available for a new user. If there are members waiting, as many as possible are assigned bikes; those in line the longest are assigned first. Then, members arriving during that minute are considered, and if more than one member arrives in a minute, they are considered one after another. For cach arrival, we check whether there is a bicycle not being used by another person. If so, the member begins to use the hicycle. If there is no unused bicycle, then the member joins the queue of people waiting for a bicycle if there are three or fewer people already waiting. If there are four people waiting, then the new arrival leaves. Note that the protocol for this simulation is for those who finish using a bicycle during a particular minute to do so before newly arrived members look for a bicycle. This is, of course, only one of several such assumptions that could be made. With the original task in mind, it is appropriate to record the total number of members who use the equipment each day, the total number who do not use it because there are four others waiting when they arrive, and the average waiting time for members who use the equipment. We assume that no member tries to use the equipment more than once a day. We will refer to members who leave without using a bicycle as disappointed. We repeat the simulation for 1000 runs, and we have the following results: Average number who try to use a bicycle = 94.60 Average number who are disappointed = 37.15 = 38.71% Average percent who are disappointed = 4.1 minutes Average waiting time The average percentage is computed by computing the percent disappointed each day and then averaging these percentages over the 30 days. This is not (necessarily) the same as the ratio of the average number who are disappointed to the average number who tried to use a bicycle. For the particular goal of this discussion, it is the average percentage of disappointed members that is of interest. In other situations, what should be noted might be the average number of disappointed members or the number (or percentage) of members who succeed in riding a bicycle. The questions that the managers of the center ask are 'What are the economic impli- cations of these results, and how do these results change if more respond to these questions, we look at the economics of the situation. Suppose the yearly membership dues for the facility are $360, or $30 per month. Also, suppose that members Ho use the stationary bikes do so ten times a month and that half of those who are dis- appointed more than three times in a month will cancel their membership. Finally, assume hat the yearly costs for purchase and maintenance of each stationary bicycle is $1200, or ipment is added?' To $100 per monthnner Can 200 CHAPTER 4 Simulation Models With these assumptions, we can investigate the economics of the current situation, Recall that the member's decision criterion results in half of the disappointed members dropping their membership if bicycles are unavailable more than 30% of the time-that is, unavailable more that three times a month, Let s be the probability that a member wll be disappointed when trying to use a bicycle on a random visit. Then, viewing multiple attempts to ride a bicycle as independent repetitions of a binomial trial with disappointment probability s, we find that the probability of four or more disappointments in a month (ten visits to the fitness center) is 1- (1 – s)10 – 10s(1 – s)º – 45s²(1 –s)% – 120s (1 - s)? (4.10) Half of the members with four or more disappointments will cancel, and the probability of this event is .5 times the expression (4.10). The economic cost to the center is $30 per month for each membership cancelled. Using the simulation results for the current situation. we estimate s as .387, so the probability that a random member who attempts to use the bicycles will cancel is ,2923, Also, we have the average number of members who attend each day-approximately 94.5 in the simulation leading to the data in Table 4.19. Thus, in this situation, the cost of cancellations is about $830 per month. This substantially exceeds the cost of installing another bicycle, and the next step is to use simulations to determine how many additional bicycles should be installed to maximize net income-that is, dues from continuing members less new costs. We repe 12 bicycles. We assume that the arrival schedules do not depend on the number of bicycles, an assumption that could be changed if there were data on which to base other assumptions about arrivals. Because the arrivals are given by a stochastic process, the average number of members who try to use bicycles varies slightly from one simulation to another. For the eight simulations reported here, that number was between 93.94 and 95.14. Using data derived from the simulations, we have the results summarized in Table 4.19. The cost and the simulation with additional stationary bicycles, using a total of 6 through revenue data in the table are monthly figures. Judging on the basis of the results shown in Table 4.19, management would achieve higher net revenue with more bicycles. The highest net revenue would be achieved for eight bicycles, although seven, eight, or nine bicycles would all give improvements of about 20% or more above the current level, Table 4.19 Percent of Disappointed Members Expected Cost of Cancellation Expected Net Cost Number of Probability of Cancellation of New Bicycles Bicycles Revenue 5. 38.7 .292 $830 $2006 6. 30.1 22.1 .177 504 $100 2231 .0804 228 2407 200 8. 15.9 .0301 86 2449 300 11.2 .0095 27 2408 2330 2234 2135 400 10 7.0 .0018 500 11 4.6 .0004 600 2.9 12 000 700 4. Repeat the analysis of the fitness center model when the assumption that half of the mem- bers who are disappointed more than three times a month will cancel their memberships is replaced by the assumption that (a)a30% of such members will cancel. CS (bar0% of such members will cancel. उ
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QUESTION 5 5 points Save Answer Historically, the average waiting time spent on hold when phoning customer service for a particular bank was one and a half minutes. To determine whether the average time people were waiting had changed since they cut the number of customer service staff, the bank undertook a random sample of the waiting time recorded by 15 customers. The results are in the Y column (in seconds) of the data file P14.12.xls which can be found in a folder under the CML Quizzes tab. Assume that the test is performed at the 5% level of significance and that the distribution of waiting times is approximately normally distributed. 1. State the direction of the alternative hypothesis used to test whether average waiting time had changed. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Calculate the test statistic correct to two decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean). 3. Use KaddStat to determine the p-value for the test correct to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that the average waiting time is not 1.5 minutes at the 5% level of significance? Type yes or no. А в с 1 Ү X1 Х2 2 28 з 43 45 49 12.6 11.4 11.5 11.1 10.4 6. 57 68 9.6 74 9 81 82 86 101 112 114 119 10 11 12 134 126 143 152 143 147 128 119 130 135 141 123 121 129 135 9.8 8.4 8.8 8.9 8.1 7.6 7.8 13 14 15 1.4 124 6.4 16 17
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