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

Question

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean sigma = 278 days and standard deviation mu = 20 days. What proportion of pregnancies lasts more than 293 days? What proportion of pregnancies lasts between 268 and 288 days? What is the probability that a randomly selected pregnancy lasts no more than 238 days? A "very preterm" baby is one whose gestation period is less than 228 days. Are very preterm babies unusual? Click the icon to view a table of areas under the normal curve. The proportion of pregnancies that last more than 293 days is (Round to four decimal places as needed.) The proportion of pregnancies that last between 268 and 288 days is (Round to four decimal places as needed.) The probability that a randomly selected pregnancy lasts no more than 238 days is (Round to four decimal places as needed.) A "very preterm" baby is one whose gestation period is less than 228 days. Are very preterm babies unusual? The probability of this event is so it be unusual because the probability is than 0.05. (Round to four decimal places as needed.)

Explanation / Answer

a) z = (x-mean)/sigma = (293-278)/20 = 0.75

P(z>0.75) is now found from normal tables as 0.2266

b) z1 = (268-278)/20 = -0.5 z2 = 0.5

P(-0.5<z<0.5) = P( z<0.5) - P(z<-0.5) = 0.691462 -0.3085 = 0.3829

c) z = (238-278)/20 = -2

P(z<-2) can be found from normal tables as 0.02275

d) z = (228-278)/20 = -2.5

P(z<-2.5) is found from normal tables as 0.00621

it is said to be unusual because probability is less than 0.05

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