Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean μ=265 days and standard deviation σ=12 days.

​(a) What proportion of pregnancies lasts more than 271 ​days?

​(b) What proportion of pregnancies lasts between 262 and 274 ​days?

​(c) What is the probability that a randomly selected pregnancy lasts no more than 244 ​days?

​(d) A​ "very preterm" baby is one whose gestation period is less than 238 days. Are very preterm babies​ unusual?

Answer 1

P(X < A) = P(Z < (A - )/)

= 265 days

= 12 days

a) P(lasts more than 271 ​days) = P(X > 271)

= 1 - P(X < 271)

= 1 - P(Z < (271 - 265)/12)

= 1 - P(Z < 0.5)

= 1 - 0.6915

= 0.3085

b) P(lasts between 262 and 274 ​days) = P(262 < X < 274)

= P(X < 274) - P(X < 262)

= P(Z < (274 - 265)/12) - P(Z < (262 - 265)/12)

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

= 0.7734 - 0.4013

= 0.3721

c) P(lasts no more than 244 ​days) = P(X < 244)

= P(Z < (244 - 265)/12)

= P(Z < -1.75)

= 0.0401

d) A value is unusual if it is more than 2 standard deviations below mean or more than 2 standard deviations above mean.

(238 - 265)/12 = -2.25

238 is 2.25 standard deviations below mean. Therefore, very preterm babies are unusual.