The length of human pregnancies from conception to birth varies according to a d

Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 263 days and standard deviation 12 days.

(a) What proportion of pregnancies last less than 270 days (about 9 months)?
(Use 4 decimal places)

(b) What proportion of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)?
(Use 4 decimal places)

(c) How long do the longest 20% of pregnancies last?
(Use 2 decimal places)


(d) What are the quartiles of the distribution of lengths of human pregnancies? (Use 2 decimal places)

Q1 =  
Q3 =

Explanation / Answer

a) proportion of pregnancies last less than 270 days =P(X<270)=P(Z<(270-263)/12) =P(Z<0.5833)=0.7202

b)proportion of pregnancies last between 240 and 270 days=P(240<X<270)=P(-1.9167<Z<0.5833)=0.7202-0.0276

=0.6925

c)for top 20 %; at 80th percentile; z=0.8416

hence corresponding length of stay =mean+z*Std deviation=273.10

d) for Q1 and Q3 ; zscore are -/+ 0.6745

hence corresponding length of Q1 =mean+z*Std deviation =254.91

corresponding length of Q3 =mean+z*Std deviation =271.09

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