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The problem involves a normally distributed dataset of pregnancy lengths, with a mean of 269 days and a standard deviation of 18 days. The task is to find the pregnancy length at the 6th percentile, which will be used to classify whether a baby is premature.

To solve this, we can follow these steps:

1. **Z-Score for the 6th percentile**: 
   The 6th percentile corresponds to a cumulative probability of 0.06. We can use the standard normal distribution to find the z-score that corresponds to this probability. Using standard z-tables or a calculator, the z-score for the 6th percentile is approximately \(-1.5548\).

2. **Convert the Z-Score to Pregnancy Length**:
   The z-score formula is:
   \[
   Z = \frac{X - \mu}{\sigma}
   \]
   where \(Z\) is the z-score, \(X\) is the pregnancy length, \(\mu\) is the mean (269 days), and \(\sigma\) is the standard deviation (18 days).

   Solving for \(X\):
   \[
   X = Z \cdot \sigma + \mu
   \]
   Plugging in the values:
   \[
   X = (-1.5548) \cdot 18 + 269
   \]
   \[
   X \approx -27.99 + 269
   \]
   \[
   X \approx 241
   \]

Thus, the length of pregnancy that separates premature babies from those not considered premature is approximately **241 days**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this problem:

1. What is the significance of the z-score in this problem?
2. How would you calculate the pregnancy length for a different percentile (e.g., the 10th percentile)?
3. How would the result change if the standard deviation of pregnancy lengths was smaller or larger?
4. Can you explain the difference between a normal distribution and a standard normal distribution?
5. What is the probability that a pregnancy lasts more than 290 days?

**Tip:** In normal distribution problems, converting between raw data values and z-scores is key to understanding probabilities and percentiles.

Lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 18 days. A baby is considered premature if the pregnancy length is at or below the sixth percentile (P6) of all pregnancy lengths. Find the length of pregnancy in days that separates the premature babies from those that are not considered premature. Round to the nearest integer.

Learn how to use the normal distribution to find the pregnancy length that separates premature babies from non-premature ones at the 6th percentile. This problem involves the use of z-scores, normal distribution, and percentile calculation. Suitable for high school students.

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