Question

If the weight (in grams) of cereal in a box of Lucky Charms is N(489,6), what is the probability that the box will contain less than the advertised weight of 466 g

Answer 1

0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.

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.

N(489,6)

This means that
`\mu = 489, \sigma = 6`

What is the probability that the box will contain less than the advertised weight of 466 g?

This is the p-value of Z when X = 466. So

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

`Z = (466 - 489)/(6)`

`Z = -3.83`

`Z = -3.83` has a p-value of 0.000064

0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.