Question

A woman in couples’ counseling was in a quandary. Her partner, Andre, was very upset because he felt that the baby his partner, Kimberly, gave birth to last month could not possibly be his baby. Kimberly is convinced that Killian is his baby and is very upset that he does not believe her. Andre’s reasoning is that he read that the average gestation for human babies is 266 days, give or take 16 days. The last time he had sexual relations with Kimberly was 307 days before Killian was born. The very next day, Andre took a job in Saudi Arabia working on an oil transport ship and did not return to Arkadelphia until two days before the birth. Killian was declared a full-term healthy infant. What is the z-score for 307 days gestation? Assume a normal distribution for the variable with a mean of 266 days, Sy = 16 days.

What percentage of babies have gestations of 307 days or greater?

What is the z-score for a baby born prematurely at 200 days gestation?

What percentage of babies have gestations of 200 days or lower?

What percentage of babies are born between 250 and 266 days gestation?

What percentage of babies are born between 250 and 285 days gestation?

What can you conclude about Kimberly’s claim? Does Andre need to cancel his upcoming scheduled appearance on the Maury Povich 2018 “Who’s your daddy?” episode airing next week?

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	266
std deviation   =σ=	16.000

percentage of babies have gestations of 307 days or greater:

probability =

P(X>307)

=

P(Z>2.56)=

1-P(Z<2.56)=

(100-99.48)%=

0.52%

2)

z-score for a baby born prematurely at 200 days gestation =(200-266)/16=-4.13

3)

percentage of babies have gestations of 200 days or lower =P(Z<-4.13) ~ 0.00%

4)percentage of babies are born between 250 and 266 days gestatio:

probability =

P(250<X<266)

=

P(-1<Z<0)=

(50.0-15.87)%=

34.13%

5)

percentage of babies are born between 250 and 285 days gestation:

probability =

P(250<X<285)

=

P(-1<Z<1.19)=

(88.3-15.87)%=

72.43%

5)as probability of happening above event means   gestation period of 307 days or more is very small but not uncertain; there is possibilty that the child belong to Andre.