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 262 days and standard deviation 17 days.

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

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

(c) How long do the longest 20% of pregnancies last? (Please use 2 decimal places.) The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75.

(d) What are the quartiles of the standard Normal distribution? (Use 2 decimal places.) Q1 = Q3 =

(e) What are the quartiles of the distribution of lengths of human pregnancies? Please use 2 decimal places. Q1 = Q3 =

Explanation / Answer

here from normal distribution z=(X-mean)/std deviation

a)P(X<270)=P(Z<(270-262)/17)=P(Z<0.4706)=0.6810

b) P(240<X<270)=P(-1.2941<Z<0.4706)=0.6810-0.0978=0.5832

c) for longest 20% time, at 80 percentile z=0.8416

hence corresponding value of time =mean +z*std deviation =276.31 days

d) for 25 percentile; z=-0.6745=Q1

and for 75 percentilez=0.6745=Q3

e)hence corresponding value =Q1=262-0.6745*17=250.53

hence corresponding value =Q3=262+0.6745*17=273.47

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