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No. By definition of the median, the median has 50 percent of the case below and 50 percent of the cases above. This has nothing to do with the cases being in a normal distribution.
The normal bilirubin count in an adult should be 0.0 mg/dL to 1.4 mg/dL. If you have a high count, it can be caused by an infection, Gilbert's syndrome, hepatitis, and cancer of the pancreas.
In the normal distribution, the mean and median coincide, and 50% of the data are below the mean.
It is 68.3%
The answer depends on what "this less than 5 percent rule" is, in contrast to some other 5 percent rule!