Question

Each bag of Skittles is supposed to have at least 30 Skittles. A machine that fills bags has a 0.005 probability of under filling a bag. For every thousand bags, what is the standard deviation for the number of bags (out of a thousand) that are under-filled. Assume the Poisson distribution.

Answer 1

Answer:

The standard deviation for the number of bags that are underfilled is 2.236.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval. The variance is the same as the mean, which mean that the standard deviation is the square root of the mean.

In this question:

Expected number of underfilled bags in a sample of n bags is:

$\mu = 0.005*n$

1000 bags, so

$\mu = 0.005*1000 = 5$

Standard deviation $S = \sqrt{5} = 2.236$

The standard deviation for the number of bags that are underfilled is 2.236.