To determine which random variable has the largest standard deviation based on the histograms, we analyze the spread of the distributions. The standard deviation measures the spread of the data around the mean, so the variable with the widest spread of values will have the largest standard deviation.

Here’s how we can analyze each histogram:

1. Random Variable X: If its values are tightly clustered around the mean, it has a smaller standard deviation.
2. Random Variable Y: If its distribution spreads further out than X but not as much as Z, it would have a medium standard deviation.
3. Random Variable Z: If its values are most widely spread from the mean, it would have the largest standard deviation.

Answer:

The random variable with the widest spread will have the largest standard deviation. If Z appears to have the widest spread in its histogram, the answer would be C) Z.

If all histograms are equally spread, then the answer would be D) All three random variables have the same standard deviation.

Finally, if the histograms do not provide enough information, E) It is impossible to tell from the histograms would be the answer.

Could you provide more details about the histograms, or clarify their visual properties? I'd be happy to refine the response further!

---

Would you like to clarify further? Here are 5 related questions to expand understanding:

1. How is the standard deviation mathematically calculated in terms of the data distribution?
2. Why does a wider spread in data indicate a larger standard deviation?
3. Can the shape of the distribution (e.g., skewness) affect standard deviation, or is it solely based on spread?
4. How does the presence of outliers affect the standard deviation in a data set?
5. Could we calculate standard deviation from raw data instead of visual histograms?

Tip: Always look for the range and density of values in a histogram when estimating measures like variance or standard deviation.