Question

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?

Answer 1

Answer:

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.