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?

1 Answer
Jan 23, 2017

213.80 <= x <= 307.20

Explanation:

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

P(Z<=(x-266)/19)=0.025
(x-266)/16=2.575 (we can get it from Normal distribution table)
x=(2.575*16)+266
x=41.2+266 =307.2

P(Z>=(x-266)/19)=0.025
(x-266)/16=-2.575
x=(-2.575*16)+266
x=-41.2+266 =213.80

Therefore the value of length is 213.80 <= x <= 307.20