Question

Last​ year, a person wrote 139 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

Mean = 0.38082 checks per day

Variance = 0.38082

Standard deviation = 0.61711

Explanation:

In a Poisson distribution, the variance (V) is equal to the mean value (μ), and the standard deviation (σ) is the square root of the variance.

A year has 365 days,, if 139 checks were written during a year, the mean number of checks written per day is:

`E(x)=\mu=(139)/(365)\\ \mu=0.38082\ checks/day`

Therefore, the variance and standard deviation are, respectively:

`V=\mu=0.38082\\\sigma=√(V)=√(0.38082)\\ \sigma =0.61711`