Question

which normal distribution has the greatest standard deviation?

Explanation:

Step1: Recall SD in normal distribution

In a normal distribution, the standard deviation (SD) determines the spread: a larger SD means a wider, flatter curve; a smaller SD means a narrower, taller curve.

Step2: Analyze the given curve

The provided curve is narrow and tall, indicating a small SD. But since the question is about which has the greatest SD (implying multiple curves, though only one is shown here—maybe a partial problem), if we assume there are other curves (e.g., wider ones not shown here), the one with the widest spread (flattest, most spread - out) would have the greatest SD. However, based on the visible curve, it's not the one with the greatest SD. But since the problem likely has multiple curves (maybe in the original context), the curve with the largest spread (widest, least peaky) would be the answer. But as the current image shows a narrow curve, the curve with the greatest SD would be the one that is wider (more spread out) than this.

Answer:

(Assuming there are multiple curves, the one with the widest spread (flattest, most horizontally extended) among the options has the greatest standard deviation. If the options include this narrow curve and others, the non - narrow (wider) one is the answer. But since only this curve is shown, more context is needed. However, based on the concept, the curve with the largest spread (widest) has the greatest SD.)