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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-07-15T10:02:10+02:00

Answer:The mean number of checks written per day = 0.3370

The standard deviation = 0.5805

The variance = 0.3370

Step-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 = 123

Let 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