MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

Answer:The mean number of checks written per day = 0.3370The standard deviation = 0.5805The variance = 0.3370Step-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 = 123Let the number of days in the year must be 365.Now, the mean number of checks written per day will be :-[tex]\lambda=\dfrac{123}{365}=0.33698630137\approx0.3370[/tex]We know that in Poisson distribution , the variance is equals to the mean value .[tex]\text{Thus , Variance }=\sigma^2= 0.3370[/tex][tex]\Rightarrow\ \sigma=\sqrt{0.3370}=0.580517010948\approx0.5805[/tex]Thus, Standard deviation = 0.5805