The lengths of nails produced in a factory are normally distributed with a mean of 4.634.63 centimeters and a standard deviation of 0.060.06 centimeters. find the two lengths that separate the top 7%7% and the bottom 7%7%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

The prbability that a normally distributed dataset with mean, μ, and standard deviation, σ, is between two values a and b is given by:



Given that the lengths of nails produced in a factory are normally distributed with a mean of 4.63 centimeters and a standard deviation of 0.06 centimeters.

To find the two lengths that separate the top 7% and the bottom 7%, Let the two required lengths be a and b, because of the symmetry of the normal curve, the probability that the length of a randomly selected nail is between these two lengths is given by:



Therefore, the two lengths that separate the top 7% and the bottom 7% are 4.54 and 4.72.