Ok, so:
We know that the width of the confidence interval decreases as the sample size increases. And, the width increases as the standard deviation increases.
So, here we can analyze that the wifth of the confidence interval depends of the sample size and the standard deviation.
So, I would say that b and d aren't correct.
The width of the confidence interval also depends of the confidence level.
Here we got the situation.
As you can see, the confidence level affects the width.
The sample size, also affects the width.
And the standard deviation also affects it.
So, the correct answer could be A. The sample mean.