Use the normal approximation to the binomial to find the fol

Use the normal approximation to the binomial to find the following: P(X 12) n=20, p=0.7

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =20 * 0.7 = 14
Standard Deviation ( npq )= 20*0.7*0.3 = 2.0494
Normal Distribution = Z= X- u / sd                   
P(X > 12) = (12-14)/2.0494
= -2/2.0494 = -0.9759
= P ( Z >-0.976) From Standard Normal Table
= 0.8354                  
P(X <= 12) = 1 - P(X > 12)
= 1 - 0.8354
= 0.1646