The lengths of nails produced in a factory are normally distributed with a mean of 5.16 centimeters and a standard deviation of 0.04 centimeters. Find the two lengths that separate the top 8% and the bottom 8%.
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5.10 cm and 5.22 cm

Explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

The top 8% corresponds with a z score of 1.41, Hence:

The bottom 8% corresponds with a z score of -1.41. Hence:

The lengths are 5.10 cm and 5.22 cm

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