The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 14 days. In what range would you expect to find the middle 68% of most pregnancies? Between and you were to draw samples of size 49 from this population, in what range would you expect to find the middle 68% of most averages for the lengths of pregnancies in the sample? If Between and
The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 14 days. In what range would you expect to find the middle 68% of most pregnancies? Between and you were to draw samples of size 49 from this population, in what range would you expect to find the middle 68% of most averages for the lengths of pregnancies in the sample? If Between and
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Understanding the Distribution of Pregnancy Lengths**
The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 14 days.
**Finding the Middle 68% Range for Most Pregnancies:**
To determine the range where you'd expect to find the middle 68% of most pregnancies, apply the empirical rule (68-95-99.7 rule), which states that approximately 68% of values lie within one standard deviation of the mean. Therefore, the range would be:
- Mean ± 1 Standard Deviation
- Calculations: 270 ± 14
**Finding the Middle 68% Range for Sample Averages:**
If you were to draw samples of size 49 from this population, and wanted to know the range where the middle 68% of most averages for the lengths of pregnancies in the sample fall, use the standard error. The standard error (SE) is given by the formula:
- SE = Standard Deviation / √Sample Size
- SE = 14 / √49 = 14 / 7 = 2
Then, apply the same empirical rule for the sample means:
- Mean ± 1 Standard Error
- Calculations: 270 ± 2
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