Question

In a recent year, an author wrote 172 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check. The probability is ________ (round to three decimal places as needed).

Answer 1

To find the probability that the author wrote at least one check on a randomly selected day, we can find the complement of the probability that he wrote zero checks using the Poisson distribution.

Step-by-step explanation:

The random variable X can be defined as the number of checks the author wrote on a randomly selected day. In this case, we are interested in finding the probability that he wrote at least one check.

To do this, we can use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given a known average rate.

The formula for the Poisson probability distribution is P(X = k) = (e^-λ * λ^k) / k!, where λ is the average rate and k is the number of events.

In this case, the average rate is 172 checks per year. To find the probability that the author wrote at least one check on a randomly selected day, we can find the complement of the probability that he wrote zero checks.

The probability of zero checks is given by P(X = 0) = (e^-172 * 172^0) / 0! = e^-172.

Therefore, the probability of writing at least one check is 1 - e^-172.