Question

The length of human pregnancies from conception to birth approximately follow a normal distribution with a mean of 266 days and a standard deviation of 16 days.

1. What proportion of pregnancies last between 240 and 270 days
2. What proportion of all pregnancies will last more than 270 days 

3. What proportion of all pregnancies will last less than 270 days 

4. Very premature pregnancies are defined to last less than 224 days. What proportion of 
pregnancies are very premature pregnancies? 

5. Using the standard normal curve, find the 70th percentile for length of human pregnancy, 
i.e., the value such that 70 percent of all pregnancy lengths fall at or below it

Answer 1

Answer)

As the data is normally distributed, we can use standard normal z table to estimate the probabilities

Mean = 266

S.d = 16

A)

P(240<x<270) = p(x<270)-p(x<240)

P(x<270)

Z = (x-mean)/s.d

Z = (270-266)/16

Z = 0.25

From z table, p(z<0.25) = 0.5987

P(x<240)

Z = (240-266)/16

Z = -1.63

P(z<-1.63) = 0.0516

Required probability is = 0.5987-0.0516 = 0.5471

B)

P(x>270)

Z = 0.25

P(z>0.25) = 0.4013

C)

P(z<0.25) = 0.5987

D)

P(x<224)

Z = (224-266)/16

Z = -2.63

P(z<-2.63) = 0.0043

E)

From z table

P(z<0.53) = 0.7019 ~ 70%

0.53 = (x-266)/16

X = 274.48