Question

The lengths of a particular​ animal's pregnancies are approximately normally​ distributed, with mean equals 274 days and standard deviation sigma equals 12 days. ​(a) What proportion of pregnancies lasts more than 280 ​days? ​(b) What proportion of pregnancies lasts between 268 and 283 ​days? ​(c) What is the probability that a randomly selected pregnancy lasts no more than 256 ​days? ​(d) A​ "very preterm" baby is one whose gestation period is less than 247 days. Are very preterm babies​ unusual?

Answer 1

(a)

Proportion of pregnancies lasts more than 280 ​days = P(X > 280)

= P[Z > (280 - 274) /12]

= P[Z > 0.5]

= 0.3085

(b)

Proportion of pregnancies lasts between 268 and 283 ​days = P[268 < X < 283]

= P[X < 283] - P[X < 268]

= P[Z < (283 - 274) /12] - P[Z < (268 - 274) /12]

= P[Z < 0.75] - P[Z < -0.5]

= 0.7734 - 0.3085

= 0.4649

(c)

Probability that a randomly selected pregnancy lasts no more than 256 ​days = P[X < 256]

= P[Z < (256  - 274) /12]

= P[Z < -1.5]

= 0.0668

(d)

Probability that gestation period is less than 247 days = P[X < 247]

= P[Z < (247 - 274) /12]

= P[Z < -2.25]

= 0.012

Since the probability is less than 0.05, preterm babies​ seems unusual.