Question

Last​ year, a person wrote 119 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 = 0.3260

The standard deviation = 0.5710

The variance = 0.3260

Explanation:

Given : The number of checks written by the person = 119

We assume that the year is not a leap year.

Thus, the number of days in the year must be 365.

Now, the mean number of checks written per​ day is given by :-

`\lambda=(119)/(365)=0.3260273972\approx0.3260`

Also, in Poisson distribution , the variance is also equals to the mean value .

`\text{Thus , Variance }=\sigma^2= 0.3260`

Then ,
`\sigma= √(0.3260)=0.570964096945\approx0.5710`

Thus, Standard deviation = 0.5710