The lengths of pregnancies are normally distributed with a mean of 268 days and
ID: 3049218 • Letter: T
Question
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 307 days or longer. b. If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
a. The probability that a pregnancy will last307days or longer is
(Round to four decimal places as needed.)
b. Babies who are born on or before ______days are considered premature.
(Round to four decimal places as needed.)
Explanation / Answer
Mean = 268 days
Standard deviation = 15 days
P(X < A) = P(Z < (A - mean) / standard deviation)
A) P(a pregnancy will last 307 days) = P(X > 307)
= 1 - P(X < 307)
= 1 - P(Z < (307 - 268)/15)
= 1 - P(Z < 2.6)
= 1 - 0.9953
= 0.0047
B) Let the babies born befor P days be considered premature
P(X < P) = 0.02
P(Z < (P - 268)/15) = 0.02
From standard normal distribution table,
(P - 268)/15 = -2.05
P = 237.28 days
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