In a major city in the northwest United States 28 of the day

In a major city in the northwest United States, 28% of the days experience some period of rain...

In a major city in the northwest United States, 28% of the days experience some period of rain. What is the probability that more than 12 days out of a random sample of 31 days experience some period of rain?

Solution

Normal Approximation to Binomial Distribution
Mean ( np ) =31 * 0.28 = 8.68
Standard Deviation ( npq )= 31*0.28*0.72 = 2.4999
Normal Distribution = Z= X- u / sd                   
P(X > 12) = (12-8.68)/2.4999
= 3.32/2.4999 = 1.3281
= P ( Z >1.328) From Standard Normal Table
= 0.0918