As the mean $\mu$ increases in a normal distribution, what happens to the graph of the normal curve?

• A. The entire curve shifts to the right along the horizontal axis without changing its shape.
• B. The curve becomes taller and narrower.
• C. The curve shifts upward along the vertical axis.
• D. The curve becomes shorter and wider.

Answer: (A)

Verified step by step guidance

1. Recall that a normal distribution is defined by two parameters: the mean (\mu) and the standard deviation (\sigma). The mean determines the center of the distribution, while the standard deviation controls the spread or width of the curve.
2. Understand that changing the mean (\mu) shifts the location of the center of the normal curve along the horizontal axis (x-axis), because the mean is the point of symmetry and the peak of the curve.
3. Recognize that changing the mean does not affect the shape of the curve, meaning the height (peak) and the spread (width) remain the same since these depend on the standard deviation (\sigma), which is unchanged.
4. Therefore, when the mean increases, the entire normal curve moves to the right along the x-axis, maintaining its shape and height.
5. Summarize that the correct interpretation is: the normal curve shifts horizontally without becoming taller, shorter, wider, or narrower.