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Normal distribution and confidence intervals

For this question, I figured I could use those confidence intervals. Since the required probability is two standard deviations from the mean, I could assume it is 2.5% of the probability. But this doesn't seem right, as it's about .2% off.

Are these intervals useless? It seems if they give such inaccurate answers we shouldn't really bother to learn them...I probably would've gotten this wrong, even though it seems the best way to do it would be to use the interval.