Appropriate to transform a "normal" distribution? I have a dataset showing normality based on the p-value in a linear regression model. However, the drop on the left side gives me pause that the data is acceptable to analyze without transformation, and could be better fit using a log-transformation. Is it appropriate to transform this data anyway because it doesn't appear that the fit is entirely appropriate as-is? The main reason I'm asking is because some of the main stakeholders in this decision claims that it is 100% unacceptable to transform data if it is shown to be "normal".
Any assistance or resources that might be able to justify my decision to transform would be helpful.


You do not need normality of your outcome variable to do linear regression, you need the residuals to be normally distributed for the inference (ie pvalues) to be appropriate, but even without that you can still use the linear regression (eg if you just want to do prediction).
Typically to assess that assumption (normality of residuals) we plot the fitted values vs the residual (which you have not shown) or perform a statistical test for normality of residuals (although those typically aren't that great).
Another thing to consider is whether it makes sense for your outcome to have normal residuals. For example could peel strength ever be negative?
It looks like there are few values of peel strength in the left tail of its distribution; perhaps this is because whatever you are using to measure peel strength has a lower level of detection, in which case you have censored data.
Also, in general, if someone says to do something or base inference on something because some quantity "looks" a certain way, your statistical warning bells should go off.
