5. The lengths of human pregnancies are approximately normally distributed, with

Question

5. The lengths of human pregnancies are approximately normally distributed, with mean = 266 days and standard deviation = 16 days. a. What proportion of pregnancies lasts more than 270 days? b. What proportion of pregnancies lasts less than 250 days? c. What proportion of pregnancies lasts between 240 and 280 days? d. What is the probability that a randomly selected pregnancy lasts more than 280 days? e. What is the probability that a randomly selected pregnancy lasts no more than 280 days? f. A “very preterm” baby is one whose gestation period is less than 224 days. Are preterm babies unusual?

Explanation / Answer

We would be using normal distribution in this case and the formula would be as mentioned below: -

z=x-/

a)

z=270-266/16

z=0.25

Looking at the z-table, we get the value as 0.59871. Value more than is 1-0.59871 = 0.40129

b)

z=250-266/16

z=-1

Looking at the z-table, we get the value as 0.15866.

c)

z=240-266/16=-1.625

Looking at the z-table, we get the value as 0.052085.

z=280-266/16=0.875

Looking at the z-table, we get the value as 0.80921.

0.80921-0.052085=0.757125

d)

z=280-266/16=0.875

Looking at the z-table, we get the value as 0.80921. Value more than is 1-0.80921 = 0.19079

e)

z=280-266/16=0.875

Looking at the z-table, we get the value as 0.80921.

f)

z=224-266/16=-2.625

Looking at the z-table, we get the value as 0.0433. Looking at the probability, it seems very less and hence they can be termed unusual.

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