Which of the following statements about curves and distributions is true?

The statement that all normal curves are bell-shaped and symmetric is indeed true. A normal curve is defined by its specific mathematical properties, characterized by its bell-shaped appearance. It exhibits symmetry about its mean, meaning that the left half of the curve mirrors the right half. This symmetry is a fundamental property of normal distributions, which also allows for the calculation of probabilities using standard deviations.

In contrast, while all normal distributions are bell-shaped and symmetric, not all bell-shaped curves are normal; there are other distributions that can exhibit a bell shape without adhering to the defining characteristics of a normal distribution. Thus, the statement regarding the properties of normal curves is foundational in statistics and helps inform various applications in analysis and interpretation of data.

Other statements present inaccuracies regarding the nature of symmetric histograms and bell-shaped curves. These nuances emphasize the importance of understanding the specific criteria that classify distributions in statistical analysis.