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- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
- Graph the following logistic function, first discussed in Example 5. Use window settings of 0,20 for x and 0,1,500,000 for y. Pt=1,200,0001+1199e-0.4tThe lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y.Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8, x = 114.6, s1 = 5.03, n = 8, y = 129.3, and s2 = 5.38. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) ,
- The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?Suppose that h(x) is the hazard function of X, and h(x)=?λ for all x. (a) Calculate the survival function S(x). (b) Derive the mean life E(X) and the mean residual life E(X-x|X>x), where E(X) is a special case of mean residual life with x=0. (c) Based on your answer in (b), do you think h(x) can be used to model human lifespan? answer a, b, and cSuppose that the time in minutes, Y , that an insect spends on a plant is exponentiallydistributed such that Y ∼Exp( 1/3)(a) Evaluate P(Y ≤3)(b) Evaluate P(Y > 4)(c) Evaluate P(2 < Y < 6)(d) What is the mean length of time that this insect spends on a plant?
- Assuming that an autoregressive model is appropriatefor the crude oil data , the estimates of a, b, and σ/√Nobtained from a standard statistical package area = 0.03, b = 0.975 , σ/√N = 0.020 , K = 220 Consequently, if the present price is 210, then the logarithmof the price at the end of another 50 trading days is a normalrandom variable. CALCULATE the values of m , v , h, and CSam was 28 inches tall on her first birthday, 50 inches tall on her 8th, and 62 inches tall on her 14th. (a) Let t represent Sam's age in years, and let h represent her height in inches. Determine the values of M, A, and k for a logistic model, h(t) = M / ( 1+ Ae-kt) , that fits the given height data. (b) What is Sam's theoretical long-term expected height? That is, what is limt➔∞h(t)? (c) At what age does the model predict that Sam will reach 95% of her expected maximum height?Since the Cobot’s gripper is a critical component, a reliability of 99% is desired for that component. The failure time, in hours, of the cobot’s gripper follows a lognormal distribution with µt=10.52 and σt= 1.44. the gripper is considered a consumable item (i.e., if failed, the gripper is replaced, not repaired. a. What is the MTTF? b. At what number of hours of use should the gripper be replaced to meet the desired 99% reliability?