Suppose that the lengths of human pregnancies are normally distributed with a mean of  days and a standard deviation of  days. Complete the following statements.

(a) Approximately  of pregnancies have lengths between
and
.

(b) Approximately
?
of pregnancies have lengths between  days and  days.

To complete these statements, we need to know the mean and standard deviation values for the normally distributed human pregnancy lengths. Let's denote:

- Mean: \( \mu \)
- Standard deviation: \( \sigma \)

The normal distribution follows the empirical rule, also known as the 68-95-99.7 rule, which helps in approximating how data falls within certain intervals around the mean:

1. **68% of data** falls within 1 standard deviation from the mean, i.e., between \( \mu - \sigma \) and \( \mu + \sigma \).
2. **95% of data** falls within 2 standard deviations from the mean, i.e., between \( \mu - 2\sigma \) and \( \mu + 2\sigma \).
3. **99.7% of data** falls within 3 standard deviations from the mean, i.e., between \( \mu - 3\sigma \) and \( \mu + 3\sigma \).

### Now, let's complete the statements:

(a) **Approximately 68% of pregnancies have lengths between \( \mu - \sigma \) and \( \mu + \sigma \).**

This statement corresponds to the 68% interval of the empirical rule.

(b) **Approximately 95% of pregnancies have lengths between \( \mu - 2\sigma \) and \( \mu + 2\sigma \).**

This statement follows the 95% interval of the empirical rule.

If you provide the mean and standard deviation values, I can give you exact numerical ranges for these intervals.

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Do you want further details or have any questions about this? Here are some related questions for further exploration:

1. What is the probability that a pregnancy lasts longer than \( \mu + 2\sigma \) days?
2. How would the percentage change if the standard deviation increased?
3. How can we use the normal distribution to estimate the probability of extreme pregnancy lengths?
4. What is the z-score of a pregnancy length at \( \mu + \sigma \)?
5. How does the shape of the normal distribution affect predictions about pregnancy lengths?

**Tip:** In a normal distribution, probabilities can be easily computed using z-scores, which help compare individual data points relative to the mean.

Suppose that the lengths of human pregnancies are normally distributed with a mean of  days and a standard deviation of  days. Complete the following statements.

(a) Approximately  of pregnancies have lengths between and .

(b) Approximately ? of pregnancies have lengths between  days and  days.

Explore how human pregnancy lengths follow a normal distribution using the 68-95-99.7 rule. Learn to estimate pregnancy length intervals based on standard deviations from the mean. This topic is suited for high school students in Grades 9-12.

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