Let n: sample size p: population proportion p^ : sample proportion. For help on calculating probabilities, check Question 3.
In this problem we want to check for normality. In other words, check to see if the "Central Limit Theorem" (CLT) holds, then calculate for the probability.
n=147 p=13%
a) Since n⋅p= [ Select ] ["147", "15.07", "19.11", "0.13"] ≥10 and n(1−p) = [ Select ] ["73.5", "127.9", "53.02", "147"] ≥10 , the CLT holds for the sample proportion p^.
b) p^~ Normal (μp^ = [ Select ] ["10", "0.80", "147", "0.13"] , σp^ = [ Select ] ["147", "0.0277", "0.0007", "0.13"] )
c) P(p^<0.11) =