The lengths of a particular? animal\'s pregnancies are approximately normally? d

Question

The lengths of a particular? animal's pregnancies are approximately normally? distributed, with mean muequals257 days and standard deviation sigmaequals20 days. ?(a) What proportion of pregnancies lasts more than 287 ?days? ?(b) What proportion of pregnancies lasts between 247 and 267 ?days? ?(c) What is the probability that a randomly selected pregnancy lasts no more than 217 ?days? ?(d) A? "very preterm" baby is one whose gestation period is less than 212 days. Are very preterm babies? unusual?

Explanation / Answer

as z score =(X-mean)/std deviaiton

a)P(X>287)=P(Z>(287-257)/20)=P(Z>1.5)=0.0668

b)

P(247<X<267)=P((247-257)/20<Z<(267-257)/20)=P(-0.5<Z<0.5)=0.6915-0.3085=0.3830

c)

here as P(X<212)=P(Z<(212-257)/20)=P(Z<-2.25)=0.0122

as probability of above event is less than 0.05 therefore very preterm babies? is unusual

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