The probability of a success on any trial of a binomial expe

The probability of a success on any trial of a binomial experiment is 20%. Find the probability that the proportion of success in a sample of 400 is less than 18%. (Round your answer(s) to 3 decimal places.) P(x< 0.18) =

Solution

Proportion ( P ) =0.2
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.2*0.8/400)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.18) = (0.18-0.2)/0.02
= -0.02/0.02= -1
= P ( Z <-1) From Standard Normal Table
= 0.159