Question

The lengths of pregnancies are normally distributed with a mean of 267 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 a. The probability 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.)

not sure about this one any help would be appreciated!

Answer 1

mean = 267

s.d. = 15

a)

P(X > 309)

Z = (X - μ) / σ
Z = (309 - 267) / 15
Z = 2.8

From Z score table

P( X > 308) = P( Z > 2.8)

P(X > 308) = 0.0026

b)

Z score at p value of . 0.0040

Z = -1.75069

Z = (X - μ) / σ
-1.75069 = (X - 267) / 15
X - 267 = -26.26035

X = 240.7396