b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that i. Exactly 4 trains will pass in 30 minutes ii. less than 2 trains will pass in an hour

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Chapter1: Combinatorial Analysis
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Question
The discrete probability distribution is given
by
1
2
3
k
2k
3k
Transcribed Image Text:Question The discrete probability distribution is given by 1 2 3 k 2k 3k
b)
It is known that an average of 5 trains
pass through Grand Central Terminal every 30
minutes. Find the probability that
i.
Exactly 4 trains will pass in 30
minutes
ii.
less than 2 trains will pass in an
hour
Transcribed Image Text:b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that i. Exactly 4 trains will pass in 30 minutes ii. less than 2 trains will pass in an hour
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As per bartleby guidelines when more than two questions are given only one has to be answered please upload others separately.
Since, first question is not complete i have answered second one for you.

(a)

Consider that X= The number of trains pass through Grand Central Terminal every 30 minutes

Then, m=5.

This situation is suitable for Poisson distribution with parameter m=5 minutes that is XB(n=15,p0.60). The, the PMF of X is,

PX=x=e-10·5xx!; x=0,1,2,.....=0; otherwise

The, the value of P[ Exactly 4 trains will pass in 30 minutes] is 

PX=4=e-5·544!=0.1755

Thus, the required probability is 0.1755

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