A chord of a circle of radius a is drawn parallel to a givenstraight line, all distances from the centre of the circle being equally likely.26.1Ta and that theShow that the expected value of the length of the chord isvariance of the length. is3aа(32 – 3T). Also show that the chance is1that12.:2the length will exceed the length of the side of an equilateral triangleinscribed in the circle

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Answered: A chord of a circle of radius a is…

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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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 24. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 24. The value of the mean is muμequals= peas. (Type an integer or a decimal. Do not round.) The value of the standard deviation is sigmaσequals= peas. (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values ofpeas or fewer are significantly low. (Round to one decimal place as needed.) Values of nothing peas or greater are significantly high. (Round to one decimal place as needed.) c. Is a result of 11 peas with green pods a result that is significantly low? Why or why not? The result ▼ is…
A gaussian curve states that its average is 452.22 and a standard deviation of 12.5. What would be a proper null Hypothesis for this? Ho 452.22 (the average) Ho 12.5 (the standard deviation) Ho = 464.72 (the average plus the standard deviation) Ho= 439.72 (the average minus the standard deviation)
Using a long rod that has length m, you are goingto lay out a square plot in which the length of eachside is m. Thus the area of the plot will be m2.However, you do not know the value of m, soyou decide to make n independent measurementsX1, X2,... Xn of the length. Assume that each Xihas mean m (unbiased measurements) and variance s2.a. Show that X2 is not an unbiased estimatorfor m2. [Hint: For any rv Y, E(Y2) ¼V(Y) + [E(Y)]2. Apply this with Y ¼ X.]b. For what value of k is the estimator X2 - kS2unbiased for m2? [Hint: Compute E(X2 - kS2).]
A simple random sample of size nequals 40 is drawn from a population. The sample mean is found to be 106.4 , and the sample standard deviation is found to be 15.4 . Is the population mean greater than 100 at the alpha equals0.025 level of significance?
The variance of the height measurements is .012 If the mean height is assumed to be2.00 What is the probability that the next height measurement will measure between ±0.45σ of 2.00 ? What about ±0.15σ of 2.00 ?
The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x<-rock$shape. Assume that the n area measurements x=(x1, x2,...,xn) are a random sample from a population with true unknown mean ? and true unknown variance ?2. Remember, let x be defined by x<-rock$shape.
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and Media
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 1090 samples is 4.3 ppm. Assume the variance is known to be 1.44. Does the data support the claim at the 0.05 level? Step 1 of 5: Enter the hypotheses: Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.
The amount of liquid in a particular group of bottles is normally distributed. The mean is 1.95 L and the standard deviation is 0.15L. If a bottle is chosen at random, find the probability that the amount of water is between 1.88 L and 2.15 L Show all work as in the lessons. Paragraph B I U = I ***
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of O°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. If 1.7% of the thermometers are rejected because they have readings that are too high and another 1.7% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. interval of acceptable thermometer readings = ɔ.
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34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.

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