Question

The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh more than 15.6 ounces

Answer 1

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.

Explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 15.0 ounces and a standard deviation of 0.2 ounces.

This means that
`\mu = 15, \sigma = 0.2`

What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?

This is 1 subtracted by the p-value of Z when X = 15.6. So

`Z = (X - \mu)/(\sigma)`

`Z = (15.6 - 15)/(0.2)`

`Z = 3`

`Z = 3` has a p-value of 0.9987.

1 - 0.9987 = 0.0013

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.