Question

Messages arrive to a computer server according to a Poisson distribution with a mean rate of 16 per hour. Determine the length of an interval of time (in seconds) such that the probability that no messages arrive during this interval is 0.78. Round your answers to one decimal place (e.g. 98.7).

Answer 1

Answer: The length of an interval of time is 0.02 seconds.

Step-by-step explanation:

Since we have given that

mean rate = 16 per hour

Probability that no messages arrive during this interval = 0.78

Let X be the Poisson distribution with parameter $\lambda=16$

$P(X=0)=0.78=e^{-\lambda T}=e^{-16T}\\\\\text{Taking log on both the sides}\\\\\ln 0.78=-16T\\\\\dfrac{\ln 0.68}{-16}=T\\\\T=0.0155$

Hence, the length of an interval of time is 0.02 seconds.