  Currently inorganic scintillator detectors are used in all commercial Time of
Flight Positron Emission Tomograph (TOF-PET) devices. The J-PET collaboration
investigates a possibility of construction of a PET scanner from plastic
scintillators which would allow for single bed imaging of the whole human body.
This paper describes a novel method of hit-position reconstruction based on
sampled signals and an example of an application of the method for a single
module with a 30 cm long plastic strip, read out on both ends by Hamamatsu
R4998 photomultipliers. The sampling scheme to generate a vector with samples
of a PET event waveform with respect to four user-defined amplitudes is
introduced. The experimental setup provides irradiation of a chosen position in
the plastic scintillator strip with an annihilation gamma quanta of energy
511~keV. The statistical test for a multivariate normal (MVN) distribution of
measured vectors at a given position is developed, and it is shown that signals
sampled at four thresholds in a voltage domain are approximately normally
distributed variables. With the presented method of a vector analysis made out
of waveform samples acquired with four thresholds, we obtain a spatial
resolution of about 1 cm and a timing resolution of about 80 ps
