Descriptive and Inferential Statistics — Test

Question 16 • Advanced Algebra: Concepts and Connections

Which normal distribution has the greatest standard deviation?

Answer

Image with description Number line labeled from 80 to 112 with a bell-shaped curve above it. The curve reaches its highest point near 96 and decreases symmetrically toward both sides, approaching the number line near 80 and 112. The distribution is centered at 96.

Image with description Number line labeled from negative 8 to 32. A smooth bell-shaped curve rises from near the number line at the left, reaches a maximum near 16, and then decreases symmetrically toward the right, approaching the number line again near 40. The distribution is centered at 16.

Image with description Number line with values from 40 to 80 and a bell-shaped curve above it. The curve reaches its highest point near 60 and decreases symmetrically toward both sides, approaching the horizontal axis near 40 and 80. The graph represents a normal distribution centered at 60.

Image with description Number line labeled from 16 to 56 with a narrow bell-shaped curve above it. The curve reaches its highest point near 32 and decreases rapidly on both sides, approaching the number line near 24 and 40. The distribution is symmetric about 32 and has a smaller spread than a typical bell curve.

Explanation

A normal distribution with a greater standard deviation is more spread out. The curve in B extends roughly from −8 to 40, a span of 48 units, which is wider than the spans shown for A, C, or D. Therefore, B has the greatest standard deviation.

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