The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. What percentage of pregnancies last between 250 and 282 days?

Question

Mathematics

Susan Rowe

22 July, 05:41

The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days. What percentage of pregnancies last between 250 and 282 days?

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Answers (1)

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Matteo Decker · Answer 1

68% of pregnancies last between 250 and 282 days

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 266

Standard deviation = 16

What percentage of pregnancies last between 250 and 282 days?

250 = 266 - 16

250 is one standard deviation below the mean

282 = 266 + 16

282 is one standard deviation above the mean

By the Empirical Rule, 68% of pregnancies last between 250 and 282 days