Question

Last​ year, a person wrote 128 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 =  $\lambda=0.3507$

$\text{Variance}(\sigma^2)=\lambda=0.3507$

$\text{Standard deviation}=0.5922$

Step-by-step explanation:

Given : A person wrote 128 checks in last year.

Consider , the last year is a no-leap year.

The number of days in ;last year = 365 days

Let X be the number of checks in one day.

Then , $X=\dfrac{128}{365}=0.350684931507\approx0.3507$

The mean number of checks written per​ day =  $\lambda=0.3507$

Now X follows Poisson distribution with parameter $\lambda=0.3507$.

Then , $\text{Variance}(\sigma^2)=\lambda=0.3507$

$\Rightarrow\sigma=\sqrt{\lambda}=\sqrt{0.3507}=0.59219929078\approx0.5922$