Suppose a simple random sample of size n 1000 is obtained f

Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a specified characteristic is p = .75.

a) What is the probability of obtaining x=780 or more individuals with the characteristic?
P(x (greater than or equal to) 780)) =
b) What is the probability of obtaining x=720 or fewer individuals with the characteristic?
P(x (less than or equal to) 720)) =

Please show work

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =1000 * 0.75 = 750
Standard Deviation ( npq )= 1000*0.75*0.25 = 13.6931
Normal Distribution = Z= X- u / sd                   
a)
P(X >= 780) = (780-750)/13.6931
= 30/13.6931 = 2.1909
= P ( Z >2.191) From Standard Normal Table
= 0.0142  
b)
P(X <= 720) = (720-750)/13.6931
= -30/13.6931= -2.1909
= P ( Z <-2.1909) From Standard NOrmal Table
= 0.0142