Question

In a recent​ year, an author wrote 191 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

Solution-:

Given : In a recent year, an author wrote 191 checks. ( i.e. in 365 days)

In recent year, an author wrote average checks in per day is

Let X: X-be number of checks he wrote in a recent year, on a randomly selected day

This situation is suitable for Poisson distribution with m=0.52

The p.m.f. of X is,

  

We find, P[on a randomly selected​ day, he wrote at least one check]

   (using p.m.f.)

  

  

Therefore, the required probability is 0.691