The lengths of pregnancies are normally distributed with a mean of 266 days and

Question

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 3%, then the baby is premature Find the length that separates premature babes rom those who are not premature Click to view page 1 of the table. Cick to view page 2 of the table. a. The probability that a pregnancy will last 309 days or longer is 23 Round to four decimal places as needed)

Explanation / Answer

Mean = 266

S.D= 15

a)

Find Z score at x=309

Z = (X - ?) / ?
Z = (309 - 266) / 15

Z = 2.86667

P - Value at z=2.86667

P(X=309) = 0.0021

b)

Z-score value at p -value of 0.03

Z = -1.88079

Z = (X - ?) / ?
-1.88079? = (X - 266) / 15

X=266+(-1.88079*15)=266-28.211=237.788

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