What proportion of pregnancies last fewer than 262 days? P(X < 262 days)

Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 16 days. A distribution of values is normal with a mean of 260 and a standard deviation of 16.

Answer 1

The mean is given as M = 260 days and the standard deviation is given as S = 16 days. We require P(X<262). First, convert the desired probability into a probability involving z-scores:

Z = (X-M) / S = (262-260)/16 = 0.125

Thus, P(X<262) = P(Z<0.125), which is equal to 0.5497. You can derive this value either from a standard normal calculator or from the average of the entries for P(Z<0.13) and P(Z<0.12) in a z-score table.

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