Question

which normal distribution has the greatest standard deviation?

Explanation:

Step1: Recall SD in Normal Dist

In a normal distribution, the standard deviation (SD) determines the spread. A larger SD means the curve is more spread out (flatter and wider); a smaller SD means it's narrower and taller.

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 (and likely there are other curves not fully shown here, but if we assume typical comparisons: the curve with the widest spread (flattest, most spread - out) has the greatest SD. However, since only one curve is shown here, maybe there were other options. But based on the concept, a normal distribution with a wider, flatter curve (more spread - out data) has a greater SD. If we consider that the curve here is narrow (small SD), the one with the greatest SD would be the one that's the most spread out (widest) among the options (even if not fully visible here, the key is the relationship between curve shape and SD: wider = greater SD, narrower = smaller SD).

Answer:

(Assuming there were other curves, the one with the widest, flattest shape. But since only one curve is shown, and if we consider typical problems, the curve that is the most spread - out (widest) among the given options has the greatest standard deviation. If the options included a wider curve, that would be the answer. For example, if there were three curves: the left (narrow), middle (medium), right (wide), the right one would be the answer. But based on the concept, the normal distribution with the greatest standard deviation is the one with the largest spread (widest curve).)