Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer:
**Normal Distribution and Its Properties:**
Normal distribution, also known as Gaussian distribution, is a fundamental concept in statistics and probability theory. It is characterized by a bell-shaped curve that is symmetric around the mean. Here are its key properties:
1. **Bell-shaped Curve:** The graph of a normal distribution is bell-shaped, with the highest point at the mean, which is also the median and mode of the distribution.
2. **Symmetry:** The distribution is symmetric around the mean, meaning that the probabilities on both sides of the mean are equal.
3. **Mean, Median, and Mode:** These three measures of central tendency are all located at the center of the distribution, which is the mean (\( \mu \)).
4. **Standard Deviation:** The spread of the distribution is determined by the standard deviation (\( \sigma \)). The larger the standard deviation, the wider the distribution.
5. **68-95-99.7 Rule:** This empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
6. **Probability Density Function:** The probability density function (pdf) of a normal distribution is given by:
\[ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]
where \( x \) is a random variable, \( \mu \) is the mean, \( \sigma \) is the standard deviation, \( \pi \) is the mathematical constant pi, and \( e \) is the base of the natural logarithm.
**Real-life Phenomenon that Follows a Normal Distribution:**
One real-life phenomenon that often follows a normal distribution is human height. Here’s why:
- **Symmetry:** Heights of people tend to follow a symmetric distribution around the average height.
- **Central Tendency:** The average height (mean) of a population can be measured and is often reported.
- **
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
