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

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

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) = (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 = √(5) = 2.236`

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