A sample of 20 specimens of soil was tested under shear, and water absorption tests.8 of them failed in shear test, while 5 was failed in water absorption test and 2 failedin both. Find the following probabilities if a random sample is selected?1-Failed in one of them at least?2-Failed in one of them at most?3-If it is failed in shear to be failed in absorption?4-If it is good in absorption to be bad in shear?

Answered: Image /qna-images/answer/d0c67e49-9daf-49e7-a848-cad5df7f12d4.jpg

Answered: A sample of 20 specimens of soil was…

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...

See similar textbooks

Similar questions

1. A test for SARS-Cov-2 has sensitivity of 0.8 and specificity of 0.7.a. A person tested positive in the test, what is the probability that they have the virus?b. A person tested negative in the test, what is the probability that they have the virus? 2. Two species of fish have similar phenotypes to each other, researchers wonder if they can classifythese fish species based on their sizes. One species has mean size of 10cm, with standard deviation of 1. Theother species has mean size of 12cm, with standard deviation of 2. Size of 15 fish from each species weremeasured.a. Which hypothesis testing method can be used to compare the mean size of the two populations? Performthe test for α = 0.01. How does result of this test help the researchers to decide if they can classify these fishspecies based on their sizes?b. What is the power of the test? How does power of the test help the researchers to decide if they can classifythese fish species based on their sizes? 3. A shopkeeper wonders…
We observe two groups of random variables: A group: X1, · ..., Xna are NĄ independent random variables with mean ua and variance 10. B group: X1, ... , Xng are ng independent random variables with mean uB and variance 40. You are interested in estimating 0 = HA - HB. (a) group, and īB, the sample mean of the B group. Come up with an unbiased estimator of 0 using A, the sample mean of the A 10 and nB (b) from part (a)? Say nA = 10. What is the mean squared error of your estimator || (c) Suppose you can choose from the following options: • NA = 20, nB = 20 • NA = 60, nB 20 || • nA 20, nB 40 Which one would result in the best estimate?
A researcher wants to compare the effectiveness of two treatments on a sample of 25 patients. What is the null hypothesis for the Wilcoxon Signed-Ranks Test?
In a certain manufacturing company, a safety engineer has conducted an observation for a period of one month. The results presented show that only 10% of the machinists wear clear goggles and 90% wear cotton gloves when grinding a piece of metal during a regular day. Assuming that this claim is right and that the workers still do not know that they are being observed, what is the chance that no more than 3 out of 7 workers will be wearing their clear goggles while grinding during a random check? 0.997 0.957 0.571
b) Suppose that Y₁, Y₂,..., Y₁0 is a random sample from a bernoulli (P) distribution. It is desired that the null hypothesis Ho: P = 0.5 against the alternative hypothesis H₁: P = 0.1 at a level of significance. If Ho is rejected when Σı Y = 1. i) Determine the level of significance. ii) Find the power of the test.
V The university data center has two main computers: computer 1 and computer 2. A new routine has recently been written for computer 1 to handle its tasks, while computer 2 is still using the preexisting routine. The center wants to determine if the processing time for computer 1's tasks is now less than that of computer 2. A random sample of 11 processing times from computer 1 showed a mean of 39 seconds with a standard deviation of 19 seconds, while a random sample of 10 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 57 seconds with a standard deviation of 20 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.05 level of significance, that μ₁, the mean processing time of computer 1, is less than μ₂, the mean processing time of computer 2? Perform a one-tailed test. Then complete the parts below. Carry your…
2. Let the following lotteries: L has prizes (0, 2, 4, 6) with equal probabilities. L' has prizes (0.1, 3, 5.9) with equal probabilities. (a) Compute the expected values of the two lotteries and verify they are the same. (b) Compute the variances of the two lotteries and verify that the second lottery has a bigger variance. (c) One would be tempted to conclude that L second order stochastically dominates L', that is, any risk averse decision maker would prefer L over L'. Not true, unfor- tunately. Consider a decision maker with the following Bernoulli utility function u(x) = 2x 3 + x if x ≤ 3 if x > 3 Verify that the decision maker is risk averse and that the decision maker prefers L' over L.
A hypothesis was tested twice using a two - tailed z- test. The first test was done with a 5% significance level while the second test using a 10% significance level. If the test stastic for both tests is - 1.75, which of the following is true? A At 5% and 10% alpha level, the null hypothesis is accepted B The null hypothesis is rejected at 5% and accepted at 10% C The null hypothesis rejected for both tests At 5% the null hypothesis is accepted and rejected at 10%
3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. * Which of these two estimators is unbiased? * Which is the better estimator, and why? %3D
It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 112 kissing couples, both people in 69 of the couples tended to lean more to the right than to the left. (Use α = 0.05.) USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 112 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. Ho: P = 2/3 H₂: P ≤ 2/3 Ho: P = 2/3 H₂: P > 2/3 O Ho: P = 2/3 H₂: P < 2/3 ⒸH₁: P = 2/3 H₂:P # 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value =

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS