The table below shows the probability distribution of the discrete random variable X. X234567P(X=x)p2pp2p3pp Find the value of p from the table above. Calculate the probability that at X is at least 5. Calculate the mean of the distribution. A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability: i).Carefully defining the random variable of interest ii). What is the probability distribution? State the values of the parameters iii). Justifying the suitability of the probability distribution identified in partiv). Calculate the probability that at most 2 bottles do not meet the company's Standards v). The expected number of bottles that do not meet the company’s standards.

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Answered: The table below shows the probability…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The table below shows the probability distribution of the discrete random variable X.

X	2	3	4	5	6	7
P(X=x)	p	2p	p	2p	3p	p

A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability:

i).Carefully defining the random variable of interest
ii). What is the probability distribution? State the values of the parameters
iii). Justifying the suitability of the probability distribution identified in part
iv). Calculate the probability that at most 2 bottles do not meet the company's Standards
v). The expected number of bottles that do not meet the company’s standards.

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