Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean

muμequals=254

days and standard deviation

sigmaσequals=20

days.

​(a) What proportion of pregnancies lasts more than 264 ​days?

​(b) What proportion of pregnancies lasts between 244 and 269 ​days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 229 ​days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 204 days. Are very preterm babies​ unusual?

Answer 1

µ = 254

a)

                               

                                = P(Z > 0.5)

                                = 1 - P(Z < 0.5)

                                = 1 - 0.6915

                                = 0.3085

b)

                                             

                                              = P(-0.5 < Z < 0.75)

                                              = P(Z < 0.75) - P(Z < -0.5)

                                              = 0.7734 - 0.3085

                                              = 0.4649

c)

                               

                                = P(Z < -1.25)

                                = 0.1056

d)

                               

                                = P(Z < -2.5)

                                = 0.0062

Since the probability is less than 0.05, this event is unusual