Is this homework for a class? If so, be sure to cite this forum with your answer.
We need to know the manual reset, or the value of the output when the input equals the setpoint. Otherwise, I will have to assume it is 100%, not a good assumption.
Setpoint conversion to percent:
Input range 5-20 bar, span is 15 bar.
11 bar - 5 bar = 6 bar. 6/15 = 40%
The output is 100% when the setpoint equals the measurement.
(15ma - 4ma)/16ma = 68.45% output.
The output will have to fall from 100% to 68.45%, or 31.25%.
A proportional band of 40% means that an input increase of 40% will result in an output decrease of 100%.
We need an output decrease of 31.25%, so we need an input increase of 31.25% x 40% = 12.5%.
The input span is 15bar. 12.5% x 15 bar + 5 bar = 3.25 bar.
So the answer is 3.25 bar if the manual reset is 100%