Question

The time for a human pregnancy is distributed

N(39, 1.54²)

weeks in the US.

a) A preterm baby is defined as a baby born earlier than 37 weeks. What percentage of babies are preterm?
Use 4 decimals.


b) A postmature baby is born after more than 41 weeks. What percentage of babies are postmature?
Use 4 decimals.


c) What percentage are neither preterm nor postmature?
Use 4 decimals.


d) My wife says those women who have the longest 3% of pregnancies must be pretty miserable. How long do their pregnancies last?
Use 2 decimals.
___________ weeks.

e) My first son was born early. In fact only 39% of babies are born earlier than he was. How many weeks was it before he was born?
Use 2 decimals.
___________weeks.

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	39
std deviation   =σ=	1.5420

probability =

P(X<37)

=

P(Z<-1.3)=

0.0968

b)

probability =

P(X>41)

=

P(Z>1.30)=

1-P(Z<1.3)=

1-0.9032=

0.0968

c)

percentage are neither preterm nor postmature =1-0.0968-0.0968=0.8064

d)

for 97th percentile critical value of z=		1.88
therefore corresponding value=mean+z*std deviation=			41.90

e)

for 39th percentile critical value of z=		-0.28
therefore corresponding value=mean+z*std deviation=			38.57