Question

Human pregnancies days follow a normal distribution with a mean of 268 days and a standard deviation of 11 days. We observe a particular female name “Kakwat” from a particular clan in North Africa. Her pregnancy was counted only for 250 days. Is Kakwat's pregnancy unusual? We consider it “unusual” if (chance of finding human pregnancy days less than “reported value of Kakwat”) < 0.001.

A. pregnancy of Kakwat is unusual since P(pregnancy days < 250 ) < 0.001

B. We cannot judge whether this clan has an unusual pregnancy or not.

C. Pregnancy of Kakwat alone not unusual, since P(pregnancy days < 268) > 0.001

D. pregnancy of Kakwat is not unusual, since P(pregnancy days < 250 ) > 0.001

Answer 1

We have X : pregnancy days follows normal distribution with mean $\mu$ = 268 days and standard deviation $\sigma$ = 11 days

We have to find P( pregnancy days < 250)

P( X < 250) = P[ ( X - $\mu$ )/ $\sigma$ < ( 250 - 268)/11]

P( X < 250) = P( Z < -1.64)

Using Z table

P( pregnancy days < 250 ) = 0.051 > 0.001

pregnancy of Kakwat is not unusual, since P(pregnancy days < 250 ) > 0.001

Option D is correct