If X is a binomial random variable having density function binom(n,p) , we approximate P(X≤k) by P(Znp,np(1−p)≤k+1/2) . Use this approximation in the following.

If X has binomial density function binom(6000,0.6) , approximate P(X≤3620) :
P(X≤3620)≐P(Za,b≤c)

Question

If   X   is a binomial random variable having density function   binom(n,p) , we approximate   P(X≤k)   by   P(Znp,np(1−p)≤k+1/2) .   Use this approximation in the following.

If   X   has binomial density function   binom(6000,0.6) , approximate   P(X≤3620) :
P(X≤3620)≐P(Za,b≤c)

anonymous · Answer

what kind of table or TI or  maple commands i need to find this: This probability is thus

P(Za,b≤c)=?

I know that A= 3600
np
b=37.9473
$$\sqrt{np*(1-p)}$$

and finally 
c= 3620.5
$$3620+\frac{ 1 }{ 2 }$$