Is that possible for a dataset to be 9% outliers? I have a dataset about solar panels' output power. After visually inspecting the data distribution, I found it is not normal distribution and is a right-skewed distribution with many zeroes. I used the interquartile range rule to detect outliers, and I found nearly 9 percent of the data is out of range. Is that possible for a dataset to have this percentage of outliers?

As the log-normal distribution is right skewed, consider applying a log transform to your data. This is particularly appropriate if the data relates to percent change as commonly occurs with economic data.
Now, apply the usual normal distribution based test.
So, if you applied the natural log function transform, namely ln(x), it is reversed by taking exp(x) function. Note, with respect to interpretation, the center of a derived confidence interval, for example now, however, relates to the median of the untransformed data.
You might wish to review the literature on the transformation of data (start with the Box-Cox method or more advanced "Bayesian analysis of the Box-Cox transformation model based on left-truncated and right-censored data) before removing data points form possibly non-normal data and therein losing data information content.
I hope this helps.
