Question

The length of human pregnancies varies according to an approximately normal distribution with a mean of 266 days and variance of 256 days. How long are the longest 2.5% of all pregnancies?

Answer 1

About 95% of any normal distribution falls within two standard deviations of the mean, so 5% falls outside this range with 2.5% to either side. In other words,

$\mathbb P(|Z|<2)=0.95\implies \mathbb P(Z>2)=0.025$

so that the longest 2.5% fall above two standard deviations from the mean.

The mean for this distribution is 266 and the standard deviation is 256, so two standard deviations above the mean corresponds to $266+2\times256=778$.

So the longest 2.5% of all pregnancies last at least 778 days (which seems ridiculous, since this is a little over 64 years... I assume this is a silly example to get a point across).