An urn contains 2 white and 8 red marbles. A marble is drawn from the urn 100 times in succession with replacement. What is the probability of drawing more than 75 red marbles?
My attempt:
$n=100, p=0.8, q=1-p=.2$
$\mu=np=80, \sigma^2=16, \sigma=4$
$Z=(X-\mu)/\sigma$
$P_B(X\geq75)=P_N(75.5<x<100.5)$
$=P_N((75.5-80)/4)<x<((100.5-80)/4)$
$=P_N(-1.125<z<5.125)$
$=.5000-(-3708)$
$=.8708$
Can someone please tell me if this working is correct?