sorry if its wrong
To determine if the data appears to be normally distributed based on the lengths of the 18 nails, we need to consider the empirical rule (or 68-95-99.7 rule) for normal distributions. This rule states:
About 68% of the data falls within one standard deviation of the mean.
About 95% falls within two standard deviations.
About 99.7% falls within three standard deviations.
Given:
Mean = 2 inches
Standard Deviation = 0.05 inches
Using the empirical rule:
68% of nails should be between 1.95 to 2.05 inches.
95% of nails should be between 1.90 to 2.10 inches.
Almost all (99.7%) should be between 1.85 to 2.15 inches.
We would then analyze the 18 nail lengths. If the majority (about 12) are within the 1.95 to 2.05 range, a majority of the rest (about 5) are within the 1.90 to 2.10 range, and maybe just one outside that range but still within 1.85 to 2.15, then the data might appear normally distributed. If the lengths are scattered much differently than this expectation, it would suggest the data is not normally distributed.
However, since you haven't provided the lengths of the 18 nails, we can't analyze them directly. Therefore, based on the given information alone:
ANSWER: It's unclear if the data is normally distributed without seeing the lengths of the 18 nails.