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?
(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.
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