Which of the following best describes the appearance of a normal probability plot that indicates the data are approximately $normally$ distributed?

• A. The points cluster at the ends and are sparse in the middle.
• B. The points lie close to a straight line.
• C. The points form a pronounced $S$-shaped curve.
• D. The points are widely scattered with no apparent pattern.

Answer: (B)

Verified step by step guidance

1. Understand that a normal probability plot (also called a Q-Q plot) is a graphical tool used to assess whether a data set follows a normal distribution.
2. Recall that if the data are approximately normally distributed, the points on the normal probability plot will lie close to a straight line, indicating that the quantiles of the data match the quantiles of a normal distribution.
3. Recognize that deviations from normality often cause the points to form patterns such as an S-shaped curve (indicating skewness) or clustering at the ends (indicating heavy tails or outliers).
4. Note that widely scattered points with no apparent pattern suggest the data do not follow a normal distribution.
5. Therefore, the best description of a normal probability plot indicating approximate normality is that the points lie close to a straight line.