The length of human pregnancies are approximately normally distributed with a me

Question

The length of human pregnancies are approximately normally distributed with a mean of 266 and a standard deviation of 16 days.

a. What percent of pregnancies last less than 250 days?

b. Babies are considered premature if they are born at the bottom 15% of length of human pregnancies. Approximately how many days is the cut off to be considered a premature baby?

c. If 200 women who have had children are chosen at random, how many women could we expect to have pregnancies that last longer than 275 days?

d. If 29 women are randomly selected and the lengths of their pregnancies are recorded, what is the probability that the mean length of pregnancies is greater than 275 days?

Explanation / Answer

= 266 = 16

a. P(X < 250) = P(Z < (250 - 266) / 16)

P(X < 250) = P(Z < -1) = 0.1587.

b. Bottom 15% have a z score of -1.0365.

X < 266 - 1.0365 * 16 = 249.416.

c. P(X > 275) = P(Z > ((275 - 266) / 16)) = P(Z > 0.5625)

= 0.2869

=> Number of women that have pregnancies that last longer than 275 days = 200 * 0.2869 = 57.38 = 57.

d. P(x' > 275)

=> P(z < ((275 - 266) / 16 * 29)) = P (z < 3.0292) = 0.0012.

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