Suppose a simple random sample of size n125 is obtained from

Suppose a simple random sample of size n=125 is obtained from a population whose size is n=10,000 and whose population proportion with a specified characteristic is p = 0.6. What is the probability of obtaining x=80 or more individuals with the characteristic? That is what is P(p 0.64)?

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =125 * 0.6 = 75
Standard Deviation ( npq )= 125*0.6*0.4 = 5.4772
Normal Distribution = Z= X- u / sd                   

P(X < 80) = (80-75)/5.4772
= 5/5.4772= 0.9129
= P ( Z <0.9129) From Standard NOrmal Table
= 0.8193                  

P(X>=80) = 1 - P(X < 80)= 1 - 0.8193 = 0.1807