12. The length of human pregnancies ar e approximately normally distributed with

Question

12. The length of human pregnancies ar e approximately normally distributed with a mean of 260 days and standard deviation of 10 days, answer the following questio nearest thousandth if needed): (Round to the a) What proportion of pregnancies last more than 250 d ays? b) What i s the probability that a random sample of 5 pregnancies last more than 250 days? c) What is the probability that a random sample of 12 pregnancies last less than 250 days? d) What is the probability that a random sample of 28 pregnancies last less than 250 days? d) What is the probability that a random sample of 40 pregnancies last less than 250 days?

Explanation / Answer

Solution

Let X be the length of the pregnancy

(a) P(X>250) = P(Z>(250-260)/10)

P(Z>-1) = 0.8413

(b) P(X>250) = P(Z>((250-260)/(10/50.5))

P(Z>-2.2361) = 0.9873

(c) P(X<250) = P(Z<(250-260)/(10/120.5))

P(Z<-3.4641) = 0.0003

(d) P(X<250) = P(Z<-5.2915) = 1

(e) P(X<250) = P(Z<-6.3246) = 1

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