The lengths of pregnancies are normally distributed with a mean of 269 days and

Question

The lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 308 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 Click to view page 1 of the table, Click to view page 2 of the table, a. The probability that a pregnancy will last 308 days or longer is 0.0047 Round to four decimal places as needed.) b. Babies who are born on bforedays are considered premature. Round to the nearest integer as needed.)

Explanation / Answer

b) P(X < x) = 0.02

or, P((X - mean)/sd < (x - 269)/15) = 0.02

or, P(Z < (x - 269)/15) = 0.02

or, (x - 269)/15 = -2.05

or, x = -2.05 * 15 + 269

or, x = 238.25

so the required days = 238

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