Problem 2. Factor N = 1004347 using Lenstra's Elliptic Curve Factorization Algorithm with starting data a, b, and A of your choice. Record the values of a, b, and A that produced a factorization of N.
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- PROBLEM 2: Average wait in minutes for the train QM3; n=12 15 4 5 9 6 12 17 10 8 13 8 16 example: of how it should be answer: PROBLEM: #colds / year n=18 subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min =10 – 0 = 10 IQR = Q3 – Q1 = 5…Question 9 How Many Social Ties Do You Have?Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. It is nearly impossible for most people to reliably list all the people they know, but using a mathematical model, social analysts estimate that, on average, a US adult has social ties with 634 people.1 A survey of 1700 randomly selected US adults who are cell phone users finds that the average number of social ties for the cell phone users in the sample was 664 with a standard deviation of 778. Does the sample provide evidence that the average number of social ties for a cell phone user is significantly different from 634, the hypothesized number for all US adults?1Hampton, K., Goulet, L., Rainie, L., and Purcell, K., ‘‘Social Networking Sites and Our Lives,” Pew Research Center, pewresearch.org, June 16, 2011. State the null and alternative hypotheses. Your answer…Question 23: The National Institute of Mental Health published an article stating that in any one-year period, approximately 9% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: Based on the hypotheses, find the following: Test Statistic = p-value = Based on the above we choose to The correct summary would be: that the true proportion of people in that city suffering from depression or a…
- Problem 1: A report states that on average Moroccan boys (12-18 years old) get a haircut 5.8 times a year. An independent researcher randomly selected 20 boys (12-18 years old) and obtained these data. 3 2 1 3 7 2 9 4 6 6 8 0 5 6 4 2 1 3 4 1 At α = 0.05, can it be concluded that the average is more than 5.8 visits per year? (Hint: use the t test)Problem 13-21 (Algorithmic) A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table: State of Nature Rezoning Approved Rezoning Not Approved Decision Alternative S1 S2 Purchase, d1 610 -190 Do not purchase, d2 0 0 If the probability that the rezoning will be approved is 0.5, what decision is recommended?Recommended decision = What is the expected profit?Expected profit = $ fill in the blank 2 thousands. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during…What are the lower bound and upper bound of the given problem 1c? Is it 0 or 1? P(x is 40 or fewer senior) = binomcdf (n=50, p=0.72, LB=?, UB=?) = 0.9260
- Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…PROBLEM 3: Quiz scores L n = 13 students 5 7 9 10 8 9 0 6 7 10 9 10 8 example of how it needs to be answered: PROBLEM: #colds / year n=18 subjects 10; 8; 5; 2; 3; 3; 3; 6; 4; 2; 4; 5; 4; 4; 1; 0; 3; 5; For computations done by hand, data must be ordered. 0 1 2 2 3 3 3 3 4 Median 4 4 4 5 5 5 6 8 10 Q1 Q3 Sample mean = =72/18 = 4 colds Sample median = 4 colds (midpoint of data) Sample mode = 3 and 4 (the value that occurs most often; this is a bimodal data set) First Quartile (approximation) = 0.25 * N = 0.25 * 18 = 4.5; If the value is not an integer, we can round it up to the nearest integer 5 à value is 3 Third Quartile (approximation) = 0.75 * N = 0.75 * 18 = 13.5 à 14 à value is 5 Range = max – min =10 – 0 = 10 IQR = Q3 – Q1 = 5 – 3 = 2…Problem 1 One of the advantages that concrete structures have over steel structures is fire resistance (which is to say, steel becomes weak when heated). The time, T, that it takes a steel girder to reach certain temperature (where its strength becomes too low to support its load) in a fire is, however, random. Suppose that for design code development, the following data have been gathered on the time T in hours: 0.736, 0.863, 0.865, 0.913, 0.915, 0.937, 0.983, 1.007, 1.011, 1.064, 1.109, 1.132, 1.140, 1.153, 1.253, 1.394 (a) Compute the values of the sample mean and the sample median by hand. (b) By how much could the smallest sample observation be increased without affecting the value of the sample median? (c) By how much could the smallest sample observation be increased without affecting the value of the sample mean? (d) Compute the values of the first quartile, third quartile, interquartile range, lower fence
- Problem 13-27 (Algorithmic) Please help me answer the questions in bold letters, #1 Expected value and #2 Expected utility, The Input Box to Question #2 is optional. In a certain state lottery, a lottery ticket costs $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies: State of Nature Win Lose Decision Alternative s1 s2 Purchase Lottery Ticket, d1 500000 -2 Do Not Purchase Lottery Ticket, d2 0 0 A realistic estimate of the chances of winning is 1 in 200,000. Use the expected value approach to recommend a decision. If required, round your answer to two decimal places.Recommended decision: Purchase Lottery Ticket Expected Value = $ (Fill in the blank) If a particular decision-maker assigns an indifference probability of 0.00001 to the $0 payoff, suppose that the following payoff table applies: State of Nature Win Lose Decision Alternative s1 s2 Purchase Lottery Ticket, d1 10…Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = f…Discrete Mathematics Problem 4 A certain virus is spreading rapidly through the population and doctors have come up with a new but imperfect test to determine if a patient is infected.• 20 percent of the population is already infected with the virus.• 90 percent of infected patients test positive.• 50 percent of healthy uninfected patients also test positive. For this section, express your answer as a simple fraction or number.i. What is the probability that a random person tests positive? ii. What is the probability that a random person who tests positive actually has the virus? iii. Suppose an independent second test is performed on a patient that previously tested positive. This time, the test result is negative. Now, what is the probability that the patient is infected with the virus?