The amount of cereal in a box is normal with mean 16.5 ounces. if the packager is required to fill at least 90% of the cereal boxes with 16 or more ounces of cereal, what is the largest standard deviation for the amount of cereal in a box?

The largest standard deviation for the amount of cereal in a box is 0.3906.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The z-score of X = 16 has a pvalue of 0.1. So it is . Now we have to find the value of .

The largest standard deviation for the amount of cereal in a box is 0.3906.

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step-by-step explanation: