2. Write the last two digits of your 1000 student ID number with a decimal point

Question

2. Write the last two digits of your 1000 student ID number with a decimal point in between these two digits: Assume that this number is the average number of squirrels you come across when you walk from the Life Science Building (LS) to the Engineering Research Building (ERB) Tomorrow you plan to walk from LS to ERB and you wonder what it the probability of observing at most three squirrels. Assume that squirrels are randomly distributed and that each squirrel is an independent observation. NOTE: if your last two digits happen to be both 0, use 4.2 as the average number of squirrels encountered.

Explanation / Answer

Solution:

Here, we have to use Poisson distribution for finding the required probability.

We are given

Mean = µ = 4.1

Formula for Poisson distribution is given as below:

P(X=x) = µx *exp(-µ)/x!

We have to find P(X3)

P(X3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

P(X=0) = 4.1^0*exp(-4.1)/0!

P(X=0) = 1* 0.016573/1

P(X=0) = 0.016573

P(X=1) = 4.1^1*exp(-4.1)/1!

P(X=1) = 4.1* 0.016573*1

P(X=1) = 0.067948

P(X=2) = 4.1^2*exp(-4.1)/2!

P(X=2) = 16.81* 0.016573/2

P(X=2) = 0.139296

P(X=3) = 4.1^3*exp(-4.1)/3!

P(X=3) = 68.921*0.016573/6

P(X=3) = 0.190371

P(X3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

P(X3) = 0.016573 + 0.067948 + 0.139296 + 0.190371

P(X3) = 0.414188

Required probability = 0.414188

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