The annual maximum load (in tons) on a structure is normal distributed with meanand standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure(R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13tons, with probabilities 0.3, 0.6, and 0.1, respectively.a) Compute the failure probability of the system in any year.b) Determine the reliability of the structure over its 30-year life span.c) Compute the expected number of failure events over the lifetime.d) Compute the safety margin and safety factor for the structure.

The annual maximum load on the structure has a normal distribution.Mean, tonsStandard deviation,…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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A soft drink dispensing machine must be adjusted if the variance of the contents o² exceeds 1.50 ml (ml² = squared milliliter). A random sample of 20 drinks from this machine has a variance of 1.90 ml². Is it sufficient sample evidence that the machine must be adjusted? Test an appropriate hypothesis at a = 0.05. Assume that the contents dispensed by the machine are approximately normally distributed. a. State null and research hypotheses about population variance o². Ho: H₁ b. Find the observed value of test statistic. Keep 3 digits after decimal point in the expression for observed value of test statistics. 2 The observed value of test statistic is bs. e. State the rejection region. The rejection region is X² c. Insert the word sufficient or insufficient into the following statement. There is be adjusted. _sample evidence to conclude that the machine must 11
The combined probability of the random variable X and Y is given below: a. Find the value of the constant. b. Calculating and interpreting the covariance and correlation of X and Y random variables. c. Calculating the expected value and variance of the random variable ? = 2? - 3? + 2
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The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.4 8.2 8.8 12.6 13.1 6.1 9.90 11.3 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H₂? Ο Α. Ho: με 11.0 H₂>11.0 O D. Ho: 11.0 H: ≤11.0 A O A. Fail to reject Ho because the P-value is greater than the significance level. OB. Reject H, because the P-value is greater than the significance level. OC. Reject Ho because the P-value is less than the significance level. OD. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A.…
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Consider a binary response variable y and a predictor variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logistic regression model, with the associated p-values shown in parentheses. Variable Intercept x LPM Logistic -6.90 (0.06) 0.19 (0.06) a. Test for the significance of the intercept and the slope coefficients at the 5% level in both models. Coefficients Intercept Slope -0.67 (0.02) 0.07 (0.03) LPM Logistic b. What is the predicted probability implied by the linear probability model for x=20 and x= 35? Note: Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places. Report the probability between 0 and 1 (not in %).
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

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