Which properties are true for a normal distribution? (Note that I didn’t say standard normal distribution.)
1. The shape of a normal distribution is symmetric, with the mean, median, and mode all being equal.
2. The distribution is bell-shaped, with the highest point at the mean.
3. The normal distribution is continuous, meaning that it can take on any value within its range.
4. The area under the curve of a normal distribution is equal to 1.
5. The distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ).
6. The distribution is defined for all real numbers.
7. The distribution is fully determined by its mean and standard deviation.
8. The distribution is unimodal, having a single peak.
9. The distribution is asymptotic, meaning that the tails of the distribution approach but never touch the x-axis.
10. The distribution is defined by the formula for the probability density function (PDF), which follows the famous "bell curve" formula: f(x) = (1/σ√(2π)) * e^(-(x-μ)²/(2σ²)), where e is the base of the natural logarithm.