Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = -4 and B = 4. (a) Compute P(X < 0). (b) Compute P(-2 < X < 2). (c) Compute P(-1
Q: decimal places.) (a) Compute a 95% CI for when n = 25 and x = 55.6. watts (b) Compute a 95% CI for μ…
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- A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.1. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 56.0. watts (b) Compute a 95% CI for μ when n = 100 and x = 56.0. watts (c) Compute a 99% CI for μ when n = 100 and x = 56.0. watts (d) Compute an 82% CI for μ when n = 100 and x = 56.0. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n =Let P=f(t)=600(1.033)t be the population of a community in year t. Evaluate f(10)A person arrives at the side of a single lane, one way street as a car passes by. Consider this time as time 0. There is no traffic lights and no pedestrian lanes in the nearby area. He stands there watching cars pass by. The number of cars to pass by within a period of time cane be modeled using a poison distribution. Suppose the cars pass by the person at a rate of 4.5 cars per minute. Assume that the cars pass by instantaneously. what is the probability that no cars pass by him within a 2 minute window b) if the person had to guess how many cars would pass by in the next five minutes, what number should he guess? Why? c) what is the distribution for the time until the first car passes by him(time is continuous). What is the expected time until the first car passes by him?
- A CI is desired for the true average stray-load loss (watts) for a certain type of induction motor when the line current held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.9. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 59.1. watts (b) Compute a 95% CI for when n = 100 and x = 59.1. watts (c) Compute a 99% CI for μ when n = 100 and x = 59.1. watts (d) Compute an 82% CI for when n = 100 and x = 59.1. watts (e) How large must n be if the width of the 99% interval for is to be 1.0? (Round your answer up to the nearest whole number.) n =The inhabitants of a city develop skin cancer at an approximate rate A. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: n ~ Poisson(X) X\n - Binomial(n, p) Question 5: What is the distribution of n X? n – X|X ~ Binomial X(1-p) 1- p We do not have enough information to answer this question. n|X Poisson(Xp) On - X|X ~ Poisson(A(1 – p) 1 for n > x n|X ~ fn|x (n|x) = n! 1- Di-o i! 0.w.Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
- 3. (Sections 4.1 and 4.3) READ CAREFULLY. The graph of y f'(x) is given. %3D (a) Use the graph to find the critical numbers of f. Explain how you found your answer(s). (b) Use the First Derivative Test to classify each of the critical numbers as locations of local maximum values of f, local minimum values of f, or neither. Give reasons for your answers. S(x). (c) ): Use your work above to sketch a possible graph of y DPlease show as many steps as you can so i can understand the proccess.Consider the function f(x) = 2/T + 6 on the interval [4, 9]. Find the average or mean slope of the function on this interval. 0.4 By the Mean Value Theorem, we know there exists a c in the open interval (4, 9) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
- The inhabitants of a city develop skin cancer at an approximate rate X. For those people who have developed skin cancer, some proportion p E (0, 1) will die from the disease. Assume a simple model such that n, the number of people who develop skin cancer, is distributed Poisson(A). Let X denote the people who die from skin cancer in this city. Then, assuming that every cancer patient is independent of the others, and that the proportion p is constant: ~ U Poisson(A) X\n - Binomial(n, p) Question 4: What is the marginal distribution of X? Hint: two primary ways to do this: 1. you can summate out n from the joint distribution directly (more straightforward, but tricky algebra) o Pay attention to the lower limit of n o Remember that i=0 2. use MGFS + iterated expectation: E[etx] = En|Exn[etx n|| and then recognize the distribution corresponding to the MGF (need to understand MGFS and iterated expectation). o Obtain the inner expectation by using the Binomial theorem. O X Binoтial(n, Ap)…Suppose that medical science has a cancer-diagnostic test that is 95% accurate on both those who do and those who do not have cancer. If 0.005 of the population actually has cancer, compute the probability that a particular individual has cancer, given that the test detected cancer.