Below n is the sample size p is the population proportion an

Below, n is the sample size, p is the population proportion, and p^ is the sample proportion. Use the central limit thorem and table to find the probablility. n = 147 p=0.13. p(0.15<p^<0.19) =

Solution

Normal Distribution
Proportion ( P ) =0.13
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.13*0.87/147)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.15) = (0.15-0.13)/0.0277
= 0.02/0.0277 = 0.722
= P ( Z <0.722) From Standard Normal Table
= 0.76486
P(X < 0.19) = (0.19-0.13)/0.0277
= 0.06/0.0277 = 2.1661
= P ( Z <2.1661) From Standard Normal Table
= 0.98485
P(0.15 < X < 0.19) = 0.98485-0.76486 = 0.22