In total he played 7 games for the Mets in 1977, getting 4 hits in 16 at-bats for a .250 batting average. He also drew 4 walks, giving him an on-base percentage of .400. Norman spent the 1978 and 1979 seasons alternating between Tidewater and the Mets. In 1978 he played 19 games for the Mets, getting his first Major League home run, and posting a batting average of .266, an on-base percentage of .284 and a slugging percentage of .484. In 1979 he played 44 games with the Mets, with a batting average of .245, an on-base percentage of .311 and a slugging percentage of .373.  1980 was Norman's only complete season in the Major Leagues. He played in 69 games for the Mets, but his batting average was a poor .185. With just 2 home runs and 6 walks, both his on-base percentage and slugging percentage were under .300. He was demoted back to Tidewater for the 1981 season. Norman played 40 games for Tidewater in 1981, with a batting average of .247. On May 29, 1981 he was traded along with pitcher Jeff Reardon to the Montreal Expos in exchange for right fielder Ellis Valentine. Norman spent the latter part of the 1981 season playing for the Montreal Expos AAA affiliate, the Denver Bears of the American Association. He played in 73 games for Denver with 11 home runs, a batting average of .272, an on-base percentage of .348 and a slugging percentage of .490. In 1982 Norman split his time between the Expos Major League team and their new AAA affiliate, the Wichita Aeros. He played in 53 games for the Expos, getting 66 at-bats. With a batting average of just .212, that was Norman's last season in the Major Leagues. He continued to bounce around the minor leagues through the 1987 season, ending his professional career at age 32.  , or Retrosheet, or Venezuelan Winter League