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

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

Answer: (C)

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 entire normal curve along the horizontal axis (x-axis) without altering its shape. This means the peak of the curve moves left or right depending on whether the mean decreases or increases.
3. Recognize that the shape of the normal curve, including its height and width, is controlled by the standard deviation \( \sigma \). Since the problem only mentions a change in the mean, the standard deviation remains constant, so the shape does not change.
4. Visualize that increasing the mean moves the center of the curve to the right, so the graph shifts right along the horizontal axis, but the curve's height and width stay the same.
5. Conclude that the correct interpretation is: as the mean increases, the normal curve shifts to the right along the horizontal axis without changing its shape.