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

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**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

**Instructions for Input:**

Enter your answers as numbers. Your answers should be accurate to one decimal place. 

For help, please use the "Message instructor" option.

**Interactive Elements:**

- A text box is provided for each part to input the range.
- A "Submit Question" button is available for response submission.
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 **Instructions for Input:** Enter your answers as numbers. Your answers should be accurate to one decimal place. For help, please use the "Message instructor" option. **Interactive Elements:** - A text box is provided for each part to input the range. - A "Submit Question" button is available for response submission.
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