# BEA140 Quantitative Methods Assignment

Added on - 15 Mar 2020

BEA140

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Quantitative Methods Assignment 3BEA140Student id[Pick the date]

Question 1(a)The given number of weeds that would be found in a kg of sample can be approximatedas Poisson distribution. The reasons are as follows.Poisson distribution is a discrete probability distribution and the number of weeds would alsobe discrete.Further, Poisson distribution is based on average incidence of successes that are knownwithin a region which is known as mean. This value is also known for the given case as 1 perkg of sample.(b)Number of seeds found in 1 kg sample = xMean value of variable = 1Probability of there being 0 seeds observed in 1kg of sample.Formula for Poisson distribution is shown below:λ=1,x=0P(X=0)=e−λλxx!=e−1100!=0.36791

Probability of there being 1 seeds observed in 1kg of sample.λ=1,x=1P(X=1)=e−λλxx!=e−1111!=0.3679Probability of there being 2 seeds observed in 1kg of sample.λ=1,x=2P(X=2)=e−λλxx!=e−1122!=0.1839Probability of there being 3 seeds observed in 1kg of sample.λ=1,x=3P(X=3)=e−λλxx!=e−1133!=0.0613(c)Probability of observing 4 or more seeds in shipment.λ=1,x=4P(X=4)=1−{P(X=0)+P(X=1)+P¿¿1−(0.3679+0.3679+0.1839+0.0613)2

¿1−0.9810¿0.0190(d)Whenλ=2,3,4Average rate of inclusion in container (seeds per kg)No of seeds detected insample123400.36790.13530.04980.018310.36790.27070.14940.073320.18390.27070.22400.146530.06130.18040.22400.19544 or more0.01900.14290.35280.5665(e)Probability of accepting a container when the inclusion rate is 4 seeds per kg¿?Probability =Probabilitythatinclusionrateis4Probabilitythatinclusionrateis4∨more=(0.01530.0190)=0.807(f)If the rate of weed seeds per kg = 2Probability of redirecting a container with inclusion rate 2 seeds per kg¿?Probability =Probabilitythatinclusionrateis2Probabilitythatinclusionrateis2∨more=(0.18390.6321)=0.29(g)It makes sense to selectively increase the testing frequency especially if the false positiveindicates presence of four weeds in the sample as the likelihood of the false positiveslying in the case of 4 is high as seems high as has been computed above.3

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