Answer:
The length of the interval during which no messages arrive is 90 seconds long.
Step-by-step explanation:
Let <em>X</em> = number of messages arriving on a computer server in an hour.
The mean rate of the arrival of messages is, <em>λ</em> = 11/ hour.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 11.
The probability mass function of <em>X</em> is:
It is provided that in <em>t</em> hours the probability of receiving 0 messages is,
P (X = 0) = 0.76
Compute the value of <em>t</em> as follows:
Thus, the length of the interval during which no messages arrive is 90 seconds long.