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)
![236 = \mu - 2\sigma = 268 - 2(16) \\300 = \mu + 2\sigma = 268 + 2(16)](https://tex.z-dn.net/?f=236%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%20268%20-%202%2816%29%20%5C%5C300%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%20268%20%2B%202%2816%29)
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.