I suspect that figure is wrong, because the Bureau of Justice Statistics does not publish the rate on prisons but on prisoners.

"As of 2016, 8.5% of the prisoners are in private for-profit prisons. Since 2000, the number of people in private prisons has increased 47%, compared to an overall rise in the prison population of 9%."

Source: https://www.sentencingproject.org/publications/private-priso...

So, if the annual increase rate has not change since 2016, as of 2019 about 9.3% of the prisoners are in for-profit jails. [edit: computed the rate, it is not "more than 10%"]