A pumping station operator observes that the demand forwater at a certain hour of the day can be modeled as anexponential random variable with a mean of 105 cfs (cubic feetper second).(a) Find the probability that the demand will exceed 200 cfs ona randomly selected day.(b) Find the probability that the demand will not exceed 200 cfsin either of the next two days.(c) What is the maximum water-producing capacity that thestation should keep on line for this hour so that the demandwill exceed this production capacity with probability of only0.01?(d) If the mean demand of water increased to 140 cfs, what isthe probability that the demand will exceed 200 cfs?

Answered: Image /qna-images/answer/3135602f-7860-48a8-b423-8ee26c37b5df.jpg

Answered: A pumping station operator observes…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a) Find the value at risk (VaR) for an investment of $400,000 at2%. (That is, find out how low the value of this investment could be if the worst 2% of outcomes are ruled out.) The investment is expected to grow during the year by 10% with SD 35%. Assume a normal model for the change in value. (b) How much smaller would the annual SD of the investment need to become in order to reduce the VaR to $100,000? Assume that the expected growth remains 10%. (a) The value at risk (VaR) for an investment of $400,000 at 2% is _____ (Round to the nearest thousand dollars as needed.) (b) The annual SD of the investment would need to become _______%. (Round to four decimal places as needed.)
(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the last several hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standard deviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below 800mm, in the absence of any climate change? Solve this problem by taking the following four steps one by one. Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we compute this probability exactly: (a) No, the population distribution is not known. (b) Yes, since the population distribution is Poisson. (c) Yes, since the population distribution is Binomial. (d) No, because no matter what the population distribution may be, it is always impossible to find the exact distribution of X 10- (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X…
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob>ChiSq 0.0013* 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
Scenario: A researcher wants to determine whether the volume of orders placed, in thousands, can predict whether an entry error was committed (yes or no). Which research analysis is most appropriate? Group of answer choices a. ANOVA b. Binary Logistic Regression c. Chi-square Contingency Table d. Non-parametric e. Regression
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A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. Suppose that during daytime hours, 60% of all vehicles are passenger cars. If 25 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X]
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4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob> ChiSq 0.0013 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
Pi- P2 Z. = %3D SE Suppose a drug company is developing a vaccine, designed to protect against a particular virus. The company states that the vaccine will be equally effective for men and women. In its initial stage, a researcher selects a random sample of 200 men and 100 women independently. At the end of the study, 15 of the men and 10 of the women showed symptoms of the virus after taking the vaccine. Is there enough evidence to conclude that there is a significant difference in the proportions of men and women who show symptoms of the virus after taking the vaccine? (a) State the appropriate hypotheses to answer this question. (b) Compute the test-statistic. (c) (i) Calculate the p-value. (ii) Interpret the p-value you have found. (d) State your conclusion in context of the situation. Page 1 135
Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y. Smoking status (S) equals 1 for at least one pack per day and 0 other- wise, alcohol consumption (A) equals the average number of alcoholic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. A. To describe the race-by-smoking interaction, construct the prediction equation when R = 1 and again when R = 0. Find the fitted YS conditional odds ratio for each case. Similarly, construct the prediction equation when S = 1 and again when S = 0. Find the fitted YR conditional odds ratio for each case. Note that, for each association, the coefficient of the cross-product term is the difference between the log odds ratios at the two fixed levels for the other variable. B. In Table 4.18, explain what the coefficients of R and S represent, for the coding as given above. What hypotheses do the P -values refer to for…

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