Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean mu μ equals = 268 268 days and standard deviation sigma σ equals = 16 16 days. ​(a) What proportion of pregnancies lasts more than 272 272 ​days? ​(b) What proportion of pregnancies lasts between 264 264 and 280 280 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 240 240 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 228 228 days. Are very preterm babies​ unusual?

Answer 1

µ = 268

a)

                               

                                = P(Z > 0.25)

                                = 1 - P(Z < 0.25)

                                = 1 - 0.5987

                                = 0.4013

b)

                                             

                                              = P(-0.25 < Z < 0.75)

                                              = P(Z < 0.75) - P(Z < -0.25)

                                              = 0.7734 - 0.4013

                                              = 0.3721

c)

                               

                                = P(Z < -1.75)

                                = 0.0401

d)

                               

                                = P(Z < -2.5)

                                = 0.0062

Since the probabilities is less than 0.05, this is unusual.