The approximate average of the histogram is 404.5 K.  From the histogram, the system varied up to 3.5 K above the average to 408.  Therefore the closest that the average could be positioned to the maximum temperature limit of 420 K, would be 416.5 K.

It is important to note that the data which was used to construct the histogram was not infinite.  That is to say that there is always a possibility that the system could vary to temperatures greater than 3.5 K above the average. 

If the maximum temperature limit was a soft constraint then this might be acceptable; however if the maximum temperature limit was a hard constraint, say for instance a safety limit, then it would not be advisable to position the average temperature so near to the limit.

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