Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute. The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately .

0.0498 = 4.98%

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.

Each minute has 60 seconds.

So a rate of 1 inquire each 4 seconds.

The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately

Mean of 1 inquire each 4 seconds, so for 12 seconds

This probability is P(X = 0).

hope this is what you were asking for!

step-by-step explanation:

could you provide figure.