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

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

Step-by-step explanation:

Normal Probability Distribution:

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

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

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

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

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.

Step-by-step explanation:

x is the third side

x² + 32² = 68²

x² = 68² - 32² = 3600

x = √3600 = 60