20 An article in International Journal of Electrical Power & Energy Systems ("Stochastic Optimal Load Flow Using aCombined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93)} considered theproblem of optimal power flow in electric power systems and included the effects of uncertain variables in theproblem formulation. The method treats the system power demand as a normal random variable with 0 meanand unit variance. What is the power demand value that is exceeded with 80% probability? Round your answerto two decimal places (e.g. 98.76).Answer is Blank 1Blank 1Addyour answer

Given: The method treats the system power demand as a normal random variable with mean 0 and unit…

Answered: An article in International Journal of…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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19. An article in International Journal of Electrical Power & Energy Systems "Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93) considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the probability that the power demand is greater than -2 and less than 2? Round your answer to three decimal places (e.g. 98.765).
A researcher would like to conduct a hypothesis test to determine if the mean age of faculty cars is less than the mean age of student cars. A random sample of 25 student cars had a sample mean age of 7 years with a sample variance of 20, and a random sample of 32 faculty cars had a sample mean age of 5.8 years with a sample variances of 16. What is the critical value of the rejection region if the difference is taken as student - faculty and the test is conducted using a 5% significance level?
14. an article in International Journal of Electrical Power & Energy Systems {"Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93)} considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the power demand value that is exceeded with 80% probability? Round your answer to two decimal places (e.g. 98.76).
A business school has a goal that the average number of years of work experience of its MBA applicants is more than three years. Historical data suggest that the variance has been constant at around six months, and thus, the population variance can be assumed to be know. Based on last years applications, it was found that among a sample of 47, the average number of years of work experience is 3.1. Can the school state emphatically that it is meeting its goal? Formulate the appropriate hypothesis test and conduct the test. What is the p-value associated with the appropriate hypothesis test for this problem?
What is the alternative of the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem?
State the variance of the critical path.
A hypothesis test on a regression coefficient fails to reject the null hypothesis at the 5% significance level. This means:
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine works properly when 24.12 ounces of liquids are dispensed. Suppose that the average amount dispensed in a particular sample of 41 bottles is 20.65 ounces with a variance of 1.48 ounces squared. What is the test statistic to test the null hypothesis that the salad dressings machine dispenses 24.12 ounces of liquid ingredients against the alternative that the salad dressings machine dispenses liquid ingredients other than 24.12 ounces?
From the article “Association of cognitive functioning with retinal nerve fiber layer thickness” by van Koolwijk et al., in Investigative Ophthalmology & Visual Science, October 2009, Vol. 50, No. 10, below is table 2 showing the results of fitting several multiple linear regression models for different response variables. Write down the fitted model corresponding to the last row of the table. You can leave the intercept as hatB0. Interpret the coefficient values corresponding to the RNFL Thickness and Male variables.
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given in the accompanying table. The researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. Which of these is an appropriate alternative hypothesis? A. H1:μfemales≠μmales B. H1:μfemales>μmales C. H1:μfemales<μmales D. H1:μfemales=μ
A quality-control technician collects a random sample of 10 rivets from each of four different suppliers and subjects them to a shear strength test to failure 1. The dependent variable in this scenario is quantitative. (enter T for true or F for false) ____ 2. The independent variable in this scenario is quantitative. (enter T for true or F for false) _____ 3. To run an ANOVA analysis in for this scenario, what is the sample size? _____
Lecturers at a university intend to see the effect of stress relief strategies such as deep breathing and relaxation techniques to the student performance in the final exam. For this reason, they assigned students of the same year in two different cohorts. More precisely, students in Cohort 1 did not do any relaxation techniques before the exam, while students in Cohort 2 performed a full range of the relaxation techniques approved by the British Psychological Society. The average mark of a random sample of 17 students from Cohort 1 was 61, with a standard deviation of 17, while the average mark of a random sample of 11 students from Cohort 2 was 67 with a standard deviation of 19. (a) Test whether the variances of marks for the two cohorts are the same at the 5% significance level. (b) Test the hypothesis that the average mark in the exam for Cohort 1 students isthe same as that for students of Cohort 2 at the 5% significance level. For this test, what is the p-value? (c) What…

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