1. The problem is to understand the normal curve, also known as the normal distribution or Gaussian distribution. 2. The formula for the normal distribution's probability density function (PDF) is: $$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$ where $\mu$ is the mean and $\sigma$ is the standard deviation. 3. Important rules: - The curve is symmetric about the mean $\mu$. - The total area under the curve is 1, representing total probability. - Approximately 68% of data lies within $\mu \pm \sigma$, 95% within $\mu \pm 2\sigma$, and 99.7% within $\mu \pm 3\sigma$. 4. To plot or analyze the normal curve, you need to know $\mu$ and $\sigma$. 5. For example, if $\mu=0$ and $\sigma=1$, the standard normal distribution is: $$f(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$$ 6. This curve peaks at $x=\mu$ and tails off symmetrically on both sides. 7. Understanding this helps in statistics for probabilities, hypothesis testing, and confidence intervals. Final answer: The normal curve is described by the PDF formula above, characterized by mean $\mu$ and standard deviation $\sigma$, with key properties of symmetry and area under the curve equal to 1.