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 309 days or longer b If the length of pregnancy s in the lowest 3%, then the baby s premature Find the length that separates premature babies from hose who are not Click to view.page 1 of the table. Click to view,page 2 of the table a. The probability that a pregnancy will last 309 days or longer is (Round to four decimal places as needed.)

Explanation / Answer

mean i.e = 269

standard deviation i.e = 15

z value = (x-)/

a)

z value for 309 is (309-269)/15 = 2.67, corresponding p value suing z table is 0.9962

P(X<309) = 0.9962

P(X>=309) = 1 - 0.9962 = 0.0038

proababilty that a pregnancy will last 309 days or longer is 0.0038

b)

let the value that seperates the premature babies from those who are not premature be L

P(X<L) = 0.03 or 3%

z value for p = 0.03 is z = -1.881

z value of L = (L-269)/15

(L-269)/15 = -1.881 => L = 269 - 15*1.881 = 240.785

Babies who are born on or before 241 days are considered premature

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