The lengths of nails produced in a factory are normally distributed with a mean of 3.34 centimeters and a standard deviation of 0.07 centimeters. Find the two lengths that separate the top 3% and the bottom 3%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

Value let separated the top 3% is T and for bottom it would be B

Now converting, we get

Based on the normal standard tables, we get

Now compare these two above equations

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

Based on the normal standard tables, we get

Now compare these two above equations

hence, for bottom it would be 3.21