Normal Approximation to the Binomial

The roulette wheel consists of 38 number, 18 red, 18 black and 2 are green. When the wheel is spun, the ball is equally likely to land on each of the 38 numbers. A gambler playing roulette and bets $10 on red each time. What is the probability that the gambler will be ahead after 100 bets?

N=100 P 18/30=.4737

np=100x.4737=47.37

n(1-p)= 1- .4737=.5263

ux=np=47.37

47.37x.5263=24.930831=4.99

x=50.5= z 50.5-47.37/4.99 =.63

Area to left is .7357

Total area 1.0000-.7357=.2643

Am I doing this right?

Thanks!