The duration of human pregnancies is not fixed. it is known that it varies according to a distribution which is roughly normal, with a mean of 266 days, and a standard deviation of 16 days. (source: figures are from moore and mccabe, introduction to the practice of statistics). according to the empirical rule (sd rule), the shortest 2.5% of pregnancies last less than how many days?

Question

Mathematics

Kylie Meyer

28 March, 18:47

The duration of human pregnancies is not fixed. it is known that it varies according to a distribution which is roughly normal, with a mean of 266 days, and a standard deviation of 16 days. (source: figures are from moore and mccabe, introduction to the practice of statistics). according to the empirical rule (sd rule), the shortest 2.5% of pregnancies last less than how many days?

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Chelsea Clay · Answer 1

By the empirical rule, 95% of the distribution is within 2 standard deviations. Since the other 5% is split equally between the two tails of the distribution, the empirical rule says 2.5% will be below - 2 standard deviations from the mean.

... 266 days - 2 * (16 days) = 234 days

The shortest 2.5% of pregnancies last less than 234 days.