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

Answered: Image /qna-images/answer/42fdc8af-1210-4be6-bb37-a7ca410bcfc7.jpg

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Similar questions

If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)
An ecologist who analyzes water samples tests the nullhypothesis that any contaminants in the water are belowdangerous concentrations. Because he uses a = 0.05, aset of samples from a small lake that produced a P-valueof 0.07 led him to conclude that the evidence did notpoint to unsafe water conditions. Which is true?A) There’s a 7% chance the lake’s water really is safe.B) There’s a 93% chance the lake’s water really is safe.C) There’s a 7% chance his sampling would have shownas much contamination as it did even if the lake’swater really is safe.D) If the lake’s water really is unsafe, there’s a 5%chance he wouldn’t notice.E) If he had taken more samples, he probably wouldhave rejected the null and concluded that the waterwas unsafe.
An employee of a bank wants to test the null hypoth-esis that on the average the bank cashes 10 bad checks per day against the alternative that this figure is too small. Ifhe takes a random sample and decides to reject the nullhypothesis if and only if the mean of the sample exceeds12.5, what decision will he make if he gets x = 11.2, andwill it be in error if(a) λ = 11.5; (b) λ = 10.0?Here λ is the mean of the Poisson population beingsampled.
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A biologist wants to test the null hypothesis that themean wingspan of a certain kind of insect is 12.3 mmagainst the alternative that it is not 12.3 mm. If shetakes a random sample and decides to accept the nullhypothesis if and only if the mean of the sample fallsbetween 12.0 mm and 12.6 mm, what decision will shemake if she gets x = 12.9 mm and will it be in error if(a) μ = 12.5 mm; (b) μ = 12.3 mm?
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An experimenter is interested in the hypothesis testing problemH0 : µ = 373 vs µ 6= 373where µ is the average breaking strength of a bundle of wool fibers. Suppose that a sampleof n = 29 wool fiber bundles is obtained and their breaking strengths are measured.(a) For what values of the t-statistic does the experimenter accept the null hypothesis with asize α = 0.10?(b) For what values of the t-statistic does the experimenter reject the null hypothesis with asize α = 0.01?Suppose that the sample mean is ¯x = 312.7 and the sample standard deviation is s = 8.13.(a) Is the null hypothesis accepted or rejected with α = 0.10? With α = 0.01?(b) Write down an expression for the p-value and evaluate it using a computer package.

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