The lengths of nails produced in a factory are normally distributed with a mean of 5.13 centimeters and a standard deviation of 0.04 centimeters. find the two lengths that separate the top 8% and the bottom 8%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

Question

Mathematics

Ian Wilkerson

15 August, 15:55

The lengths of nails produced in a factory are normally distributed with a mean of 5.13 centimeters and a standard deviation of 0.04 centimeters. find the two lengths that separate the top 8% and the bottom 8%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

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Caroline Wong · Answer 1

The standard normal table starts at. 5 for z=0, meaning its giving us the integral of the standard gaussian from negative infinity to some positive z. We look for a table entry of 1-.08=.92 and find that at z=1.41.

We knew it was between one and two because the 68-95-99.7 rule tells us one sigma gives a probability of (100-68) / 2=16% and two sigma 2.5%, and 8% is in between those.

So our lengths at the ends of the range are

5.13 - 1.41 (0.04) = 5.0736

5.13 + 1.41 (0.04) = 5.1864

Rounding, 5.07 to 5.19