Question

The number of imperfections in a particular type of wood has an average and variance of 1.5 imperfection in 10 cubic metres of the wood. Find the probability that a 10 cubic metre block of wood has at most one imperfection by hand and verify using MATLAB.

Answer 1

Let X be the number of imperfections in a particular type of wood has in 10 cubic metres of the wood. We are given that the number of imperfections has an average and variance of 1.5 . We know that a Poisson random variable has its mean equal to the variance. Additionally, the number of imperfections has discrete values.  Hence number of imperfections can be modeled using a Poisson process.

This means that we can say X has a Poisson distribution with parameter,

the probability that a 10 cubic metre block of wood has X=x imperfections is

the probability that a 10 cubic metre block of wood has at most one (which is 1 or less) imperfection is

ans: the probability that a 10 cubic metre block of wood has at most one imperfection is 0.5578

matlab code to calculate this

get this

The probability calculated manually matches the one from matlab

code in text format

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%using the matlab builtin
prob=poisscdf(1,1.5);
fprintf('the probability that a 10 cubic metre block of wood has at most one imperfection is %.4f\n',prob);
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