Question

12 Required information The number of large packages delivered by a courier service follows a Poisson distribution with a rate of 5 per day. Let Xbe the number of large packages delivered on a given day. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Part 5 of 5 Find ox points σχε

Answer 1

This is a question of poisson distribution with
$Rate (\lambda) = 5$
For a Poisson Distribution
$P(X=x) = \frac{e^{-\mu} \mu^{x}}{x!}$
time (t) = 1

Since we know that for poisson distribution
$Mean (\mu) = \lambda t = 5.0*1.0 = 5.0$

Since, we know that variance of poisson distribution is equal to the rate of the distribution
i.e. $Variance = \lambda$
or variance is equal to the mean of the distribution

This implies that
Variance = mean
Variance = 5.0
Also, Standard deviation is equal to the square root of the variance.
$\\Standard\; deviation(\sigma_x) = (variance)^{\frac{1}{2}}=(mean)^{\frac{1}{2}}=(5)^{\frac{1}{2}}=\textbf{2.2361}$