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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-07-15T09:56:58+02:00

Answer: The mean number of checks written per day = 0.3260

The standard deviation = 0.5710

The variance = 0.3260

Step-by-step explanation:

Given : The number of checks written by the person = 119

We 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