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?

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

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Answer 1 · 2017-01-23T04:01:00

#213.80 <= x <= 307.20#

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#