A robotic inspection system uses a proximity sensor to evaluate the height of stacked packages and raise an alert if there is a deviation from the target height of 10.0 cm.

To assess performance, engineers run 20 trials at various deviations from the standard height and record whether the system triggers an alert. They record the following alert frequencies for height differences from the reference (in mm):

Δh=[0.5,0.7,0.9,1.1,1.3,1.5]

and corresponding alert rates (%): [5,25,45,75,85,95]

Fit a logistic psychometric curve to these data and estimate the 50% detection threshold (i.e., the system’s effective JND in mm).

Give your answer as X.XX mm