The weights of items produced by a company are normally distributed with a mean of 5 ounces and a standard deviation of 0.2 ounces. What is the minimum weight of the heaviest 9.85% of all items produced?

The minimum weight of the heaviest 9.85% of all items produced is 5.26 ounces.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

What is the minimum weight of the heaviest 9.85% of all items produced?

This is the 100 - 9.85 = 90.15th percentile, which is X when Z has a pvalue of 0.9015. So X when Z = 1.29.

The minimum weight of the heaviest 9.85% of all items produced is 5.26 ounces.

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