We present the discovery and follow-up observations of 142 pulsars found in the Parkes 20-cm multibeam pulsar survey of the Galactic plane . These new discoveries bring the total number of pulsars found by the survey to 742 . In addition to tabulating spin and astrometric parameters , along with pulse width and flux density information , we present orbital characteristics for 13 binary pulsars which form part of the new sample . Combining these results from another recent Parkes multibeam survey at high Galactic latitudes , we have a sample of 1008 normal pulsars which we use to carry out a determination of their Galactic distribution and birth rate . We infer a total Galactic population of 30000 \pm 1100 potentially detectable pulsars ( i.e . those beaming towards us ) having 1.4-GHz luminosities above 0.1 mJy kpc ^ { 2 } . Adopting the Tauris & Manchester beaming model , this translates to a total of 155000 \pm 6000 active radio pulsars in the Galaxy above this luminosity limit . Using a pulsar current analysis , we derive the birth rate of this population to be 1.4 \pm 0.2 pulsars per century . An important conclusion from our work is that the inferred radial density function of pulsars depends strongly on the assumed distribution of free electrons in the Galaxy . As a result , any analyses using the most recent electron model of Cordes & Lazio predict a dearth of pulsars in the inner Galaxy . We show that this model can also bias the inferred pulsar scale height with respect to the Galactic plane . Combining our results with other Parkes multibeam surveys we find that the population is best described by an exponential distribution with a scale height of 330 pc . Surveys underway at Parkes and Arecibo are expected to improve the knowledge of the radial distribution outside the solar circle , and to discover several hundred new pulsars in the inner Galaxy .