Which of the following histograms best represents a normal distribution $N(\mathrm{bc},{\mathrm{c3}}^2)$?

• A. A histogram that is symmetric and bell-shaped, with most data concentrated in the center and frequencies tapering off equally on both sides.
• B. A histogram that is skewed to the right, with a long tail extending toward higher values.
• C. A histogram that is bimodal, with two distinct peaks separated by a valley.
• D. A histogram that is uniform, with all bars approximately the same height across the range.

Answer: (A)

Verified step by step guidance

1. Understand the characteristics of a normal distribution: it is symmetric, bell-shaped, and has most data concentrated around the mean, with frequencies tapering off equally on both sides.
2. Examine each histogram option and check for symmetry: a normal distribution histogram should look the same on the left and right sides of the center.
3. Look for the shape of the histogram: the normal distribution should have a single peak (unimodal) in the center, not multiple peaks or flat regions.
4. Identify the spread of the data: in a normal distribution, the frequencies decrease gradually and evenly as you move away from the center, forming the classic bell shape.
5. Compare these features to the given options and select the histogram that matches the symmetric, bell-shaped pattern with a single central peak and tapering tails.