Question

Last​ year, a person wrote 123 checks. Let the random variable x represent the number of checks he wrote in one​ day, and assume that it has a Poisson distribution. What is the mean number of checks written per​ day? What is the standard​ deviation? What is the​ variance?

Answer 1

Answer:The mean number of checks written per​ day = 0.3370

The standard deviation = 0.5805

The variance = 0.3370

Step-by-step explanation:

Let the random variable x represent the number of checks he wrote in one​ day.

Given : The number of checks written in last year = 123

Let the number of days in the year must be 365.

Now, the mean number of checks written per​ day will be  :-

$\lambda=\dfrac{123}{365}=0.33698630137\approx0.3370$

We know that in Poisson distribution , the variance is equals to the mean value .

$\text{Thus , Variance }=\sigma^2= 0.3370$

$\Rightarrow\ \sigma=\sqrt{0.3370}=0.580517010948\approx0.5805$

Thus,  Standard deviation = 0.5805