A steel cable consists of eight high-strength steel strands. The strength of each strand can be modeled by a lognormal random variable with a mean value of 50 kips and a coefficient of variation of 10%. What is the probability that the weakest strand will have a strength less than 40 kips? Compute the same probability if the cable consists of 16, 32, and 64 strands.

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Answered: A steel cable consists of eight…

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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Three university administer the same comprehensive examination to the receipients of MS degree in Business Statistics. From each institution, a random sample of MS receipients was selected, and these receipients were then given to the exam. The following tabel shows the scores of each student from the three universities Uni A Uni B Uni C 89. 60. 81 95. 95. 70 75 89 90 92 80 78 99 66 77 At a= 0.01 , test to see if there is a significant difference in the average scores of students from the three universities Answer needed ASAP.
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a simple random sample of 800 households will be selected from the population. What is the random variable in this narrative?
What is the expected value for the number of defective LCDs3 10 2) 0.1 3) 0.45 4) 0.5 5) 0.9 06) 1
A professional basketball star who had a reputation for being a poor free throw shooter made 5210 of the 9721 free throws that he attempted, for a success ratio of 0.536. A simulation was developed to generate random numbers between 1 and 1000. An outcome of 1 through 536 was considered to be a free throw that is made, and an outcome of 537 through 1000 was considered to be a free throw that is missed. The list below shows the results for five generated numbers where 1 represents a free throw that was made and 0 represents a free throw that was missed. Complete parts (a) and (b). a. Is the proportion of successful free throws P from the simulation reasonably close to the value of 0.536? (Hint: A proportion is said to be "reasonably close" if it is within the given success ratio ± the probability of a single event.) No, P is not reasonably close to the value of 0.536. Yes, P is reasonably close to the value of 0.536. 0 1 1 1 b. The simulation was conducted 10 times to generate five…
A small river is found to be polluted due to the chemical waste from two major industries, A and B. Due to the strict standards enforced by the EPA, the probability of controlling the pollutions from A and B are 0.7 and 0.85, respectively, in the next two years. It is estimated that, if only one of the industries complies with the strict standards of EPA, there is a 75 percent probability of controlling the pollution in the river to an acceptable level. (a) Find the probability of controlling the pollution in the river in the next two years. (b) If the pollution in the river is not controlled in the next two years, what is the probability that it is caused entirely by industry A?
A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).
Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F). 21.0 15.1 19.0 17.6 17.5 15.5 14.7 17.1 y 87.8 71.4 94.1 84.7 81.4 75.2 69.7 82.0 15.4 16.2 15.0 17.2 16.0 17.0 14.4 69.4 83.3 79.6 82.6 80.6 83.5 76.3 Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answer to four decimal places.) %3D X = y = + %3D Find the value of the coefficient of determination r. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to four decimal places. Round your…
After careful research you observe that the number of hackers active on each day is a random variable Bin(3,0.5) distribution. If no hackers are active, the probability of the website failure is 0.15; If one hacker is active the probability of the website failure is 0.3; if two or more hackers are active the probability of the website failure is 0.5. You conclude that the total probability of website failure on a given day is two decimal place). Assuming there is a failure, the probability no hackers are active is (to (to two decimal places).
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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