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The mean length of a human pregnancy is 268 268 ​days, with a standard deviation of 16 16 days. Use the empirical rule to determine the percentage of women whose pregnancies are between 236 236 and 300 300 days.​ (Assume the data set has a​ bell-shaped distribution.)

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Answer:

95% of women have pregnancies length between 236 and 300 days.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 268

Standard Deviation, σ = 16

We are given that the distribution of  length of a human pregnancy is a bell shaped distribution that is a normal distribution.

Empirical Rule:

  • It states that for a normal distribution all the data lies within three standard deviation of mean.
  • About 68% of data lies within one standard deviation of mean.
  • About 95% of data lies within two standard deviations of mean,
  • About 99.7% of data lies within three standard deviation from mean.

P(pregnancies are between 236 and 300 days)

[tex]236 = \mu - 2\sigma = 268 - 2(16) \\300 = \mu + 2\sigma = 268 + 2(16)[/tex]

By empirical rule, 95% of data lies within two standard deviations of mean, thus, 95% of women have pregnancies length between 236 and 300 days.

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