Question

1.  The gestation period (length of pregnancy) for male babies born in New York is normally distributed with a mean of 39.4 weeks and a standard deviation of 2.3 weeks.

(a)  What percent of mothers of male babies are pregnant for less than 35 weeks?

(b)  What percent of mothers of male babies are pregnant for between 35 and 40 weeks?

3. What percent of mothers of male babies are pregnant for more than 40 weeks?
4.   Suppose a sailor had shore leave 46 weeks ago and his wife is delivering a baby today.  What should the sailor say to his wife when he gets home?

Answer 1

(a)

= 39.4

= 2.3

To find P(X < 35):

Z = (35 - 39.4)/2.3

= - 1.9130

By Technology, Cumulative Area Under Standard Normal Curve = 0.0279

So,

P(X<35) = 0.0279

So,

Answer is:

0.0279

(b)
To find P(35 < X < 40):

For X =35:

Z = (35 - 39.4)/2.3

= - 1.9130

By Technology, Cumulative Area Under Standard Normal Curve = 0.0279

For X =40:

Z = (40 - 39.4)/2.3

= 0.2609

By Technology, Cumulative Area Under Standard Normal Curve = 0.6029

So,

P((35 < X < 40) = 0.6029 - 0.0279 = 0.5750

So,

Answer is:

0.5750

(c)

To find P(x>40):

Z = (40 - 39.4)/2.3

= 0.2609

By Technology, Cumulative Area Under Standard Normal Curve = 0.6029

So,

P(X>40) = 1 - 0.6029 = 0.3971

So,

Answer is:

0.3971

(d)

To find P(x>46):

Z = (46 - 39.4)/2.3

= 2.8696

By Technology, Cumulative Area Under Standard Normal Curve = 0.9979

So,

P(X>46) = 1 - 0.9979 = 0.0.0021

Since the probability = 0.21 % < 5%, it is a rare event.

So,

Suppose a sailor had shore leave 46 weeks ago and his wife is delivering a baby today. The sailor should say to his wife when he gets home that getting a child after such a long time of 46 weeks is a rare event and you should have got a child much before.