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?

Verified Answer :

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).