The lengths of a particular animal's pregnancies are approximately normally distributed, with mean muequals 271 days and standard deviation sigmaequals 8 days.
(a) what proportion of pregnancies lasts more than 275 days?
(b) what proportion of pregnancies lasts between 267 and 273 days?
(c) what is the probability that a randomly selected pregnancy lasts no more than 261 days?
(d) a "very preterm" baby is one whose gestation period is less than 253 days. are very preterm babies unusual?

A. 0.3085

B. 0.3829

C. 0.1056

D. 0.0122. Yes, "very preterm" babies are unusual.

Step-by-step explanation:

A random variable X distributed approximately normal with mean mu = 271 and standard deviation sigma = 8, can be standardized by the transformation Z = (X - mu) / sigma. In this way:

For X = 275 you have Z = (275 - 271) / 8 = 0.5

For X = 267 you have Z = (267 - 271) / 8 = -0.5

For X = 273 you have Z = (273 - 271) / 8 = 0.25

For X = 261 you have Z = (261 - 271) / 8 = -1.25

For X = 253 you have Z = (253 - 271) / 8 = -2.25

A. P (X> 275) = P (Z> 0.5) = 0.3085

B. P (267 <X <275) = P (-0.5 <Z <0.5) = 0.3829

C. P (X <= 261) = P (Z <= -1.25) = 0.1056

D. P (X <= 253) = P (Z <= -2.25) = 0.0122. Yes, "very preterm" babies are unusual.