Let x be a binomial random variable with n = 20 and p = 0.1.(a) Calculate P(x s 5) using the binomial formula. (Round your answer to five decimal places.)(b) Calculate P(x s 5) using Table 1 in Appendix I. (Round your answer to three decimal places.)(c) Use the following Excel output given to calculate P(x s 5). (Round your answer to four decimal places.)123410P(x)0.12160.27020.28520.19010.08980.03190.00890.00200.00040.00010.000011121314151617181920P(x)7E-075E-084E-092E-109E-12ЗЕ-138E-152E-162E-181E-20Compare the results of part (a), part (b), and part (c).O When rounded to two decimal places, the results of part (a), part (b), and part (c) agree with each other.O When rounded to two decimal places, the results of part (a), part (b), and part (c) disagree with each other.(d) Calculate the mean and standard deviation of the random variable x. (Round your standard deviation to four decimal places.)a - 1.3416(e) Use the results of part (d) to calculate the intervals ut o, u ± 20, and u + 30. (Round your answers to three decimal places.)0.658to 3.342-0.684X to 4.684H+ 30x to 6.026-2.026Find the probability that an observation will fall into each of these intervals. (Round your answers to three decimal places.)P(u - asxS u + a) =P(u - 20 sx u+ 20) =P(u - 30 sxs u + 30) =

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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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Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)
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Two coins are taken at random (without replacement) from a bag containing 6 nickels, 5 dimes, and 4 quarters. Let X denote the random variable given by the total value of the two coins. Find E(X). (Round your answer to four decimal places.)
A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim? Let d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs)d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs). Use a significance level of α=0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs. Golfer 1 2 3 4 5 6 7 8 Score (old design) 93 86 84 96 89 81 92 94 Score (new design) 91 90 80 92 91 77 89 87 Step 1 of 5:State the null and…
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