# The length of human pregnancies from conception to birth varies according to a distribution that is normal with mean 266 days and standard deviation 16 days. Between what values do the lengths of the middle 95% of all pregnancies fall?

## How short are the shortest 2.5% of all pregnancies? How long are the longest 2.5% all pregnancies?

Jan 23, 2017

$213.80 \le x \le 307.20$

#### Explanation:

Probability of Z score between middle 95% is 0.025 each side.

$P \left(Z \le \frac{x - 266}{19}\right) = 0.025$
$\frac{x - 266}{16} = 2.575$ (we can get it from Normal distribution table)
$x = \left(2.575 \cdot 16\right) + 266$
$x = 41.2 + 266 = 307.2$

$P \left(Z \ge \frac{x - 266}{19}\right) = 0.025$
$\frac{x - 266}{16} = - 2.575$
$x = \left(- 2.575 \cdot 16\right) + 266$
$x = - 41.2 + 266 = 213.80$

Therefore the value of length is $213.80 \le x \le 307.20$