The lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 12 days. What percentage of pregnancies last beyond 264.4 days?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Title: Statistical Analysis of Pregnancy Durations**
**Introduction:**
The lengths of pregnancies in a small rural village are analyzed under the assumption that they are normally distributed. This analysis is based on a mean duration of 262 days and a standard deviation of 12 days.
**Question:**
What percentage of pregnancies last beyond 264.4 days?
**Detailed Explanation:**
- The problem requires the calculation of the probability for a pregnancy to extend beyond 264.4 days.
- Using the properties of the normal distribution, this probability can be found by calculating the z-score for 264.4 days and then finding the corresponding percentage from standard normal distribution tables.
**Calculation Steps:**
1. **Calculate the Z-score:**
The Z-score is calculated using the formula:
\[
Z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the value of interest (264.4 days),
- \( \mu \) is the mean (262 days),
- \( \sigma \) is the standard deviation (12 days).
2. **Interpret the Result:**
- Use the Z-score to find the corresponding probability from the standard normal distribution table.
- Subtract this probability from 1 to find the percentage of pregnancies lasting beyond 264.4 days.
By following these steps, educators can help students understand how to interpret and manipulate the normal distribution in the context of real-world data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24a3da1e-8078-4e69-95e8-f18f95f918aa%2F547a6d89-eed3-4fad-b366-c7c6b579df39%2Fz81y4kr_processed.jpeg&w=3840&q=75)
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