The lengths of pregnancies are normally distributed with a mean of 267 days and

Question

The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days a Find the pr bab ty o a pregnancy lasting 309 days or longer b lf he length of pregnancy is in the lowest 3% 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 paga 2 of the table a. The probabllity that a pregnancy will last 309 days or longer is Round to four decimal places as needed.) b. Babies who are born on or before days are considered premature. Round to the nearest integer as needed.)

Explanation / Answer

Mean = 267

Sd = 15

A) P(X > 309) = P(Z > (309 - 267)/15)

= P(Z > 2.8)

= 1 - P(Z < 2.8)

= 1 - 0.9974

= 0.0026

B) P(X < x) = 0.03

Or, P(Z < (x - 267)/15) = 0.03

Or, (x - 267)/15 = - 1.88)

Or, x = 267 - 1.88 * 15

Or, x = 238.8

Or, x = 239

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