The probability that only one phone call passes through a given minute, provided that the relay follows a Poisson distribution with a mean of 5 is 0.033689.
Here it is given that the number of phone calls that pass through a particular cell phone relay system follows a Poisson distribution. The time interval given here is of a minute.
For any Poisson distribution
P(X = x) = λˣ X e^(-λ) / x!
where λ = mean of the distribution.
x = the no. of times the event occurs in the time interval.
It is given that
λ = 5 calls per minute.
We need to find the probability that only n a given minute, the relay receives only one phone call.
Hence, x = 1
Therefore, the probability that only one phone call passes through in a given minute is
P(X = 1) = 5¹ X e^(-5) / 1!
= 0.033689
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