Long description: figure1
Alt text: A graph shows two normal distribution curves, one centered at \(\text{X} \text{ ~} \text{N}(\text{μ}, \text{σ}^2)\) and the other centered at \(\bar{\text{X}} \text{ ~} \text{N}(\text{μ}, \frac{\text{σ}^2}{n})\).
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- The graph displays two distinct probability density functions plotted against a horizontal axis labeled \(\text{μ}\).
- The curve on the right is labeled \(\text{X} \text{ ~} \text{N}(\text{μ}, \text{σ}^2)\), representing a normal distribution with a mean of \(\text{μ}\) and a variance of \(\text{σ}^2\).
- The curve on the left is labeled \(\bar{\text{X}} \text{ ~} \text{N}(\text{μ}, \frac{\text{σ}^2}{n})\), representing a normal distribution with the same mean \(\text{μ}\) but a smaller variance of \(\frac{\text{σ}^2}{n}\), where \(n\) is the sample size.
- A vertical dashed line is drawn passing through the mean \(\text{μ}\), indicating the center for both distributions.