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?
Accepted Solution
A:
Answer: The mean number of checks written per day = 0.3260The standard deviation = 0.5710The variance = 0.3260Step-by-step explanation:Given : The number of checks written by the person = 119We 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 :-[tex]\lambda=\dfrac{119}{365}=0.3260273972\approx0.3260[/tex]Also, in Poisson distribution , the variance is also equals to the mean value .[tex]\text{Thus , Variance }=\sigma^2= 0.3260[/tex]Then , [tex]\sigma= \sqrt{0.3260}=0.570964096945\approx0.5710[/tex]Thus, Standard deviation = 0.5710