The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 309 days or longer. b. If the length of pregnancy is in the lowest 4 %, then the baby is premature. Find the length that separates premature babies from those who are not premature.
Solution :
Given that ,
a) P(x
309 ) = 1 - P(x
309)
= 1 - P[(x - ) /
(309 - 266) / 15]
= 1 - P(z
2.87 )
= 1 - 0.9979
= 0.0021
b) Using standard normal table,
P(Z < z) = 4%
= P(Z < z ) = 0.04
= P(Z < -1.75 ) = 0.04
z = -1.75
Using z-score formula,
x = z *
+
x = -1.75 * 15 + 266
x = 239.75
x = 240 days
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