A random sample of size n 200 is taken from a population wi

A random sample of size n = 200 is taken from a population with population proportion P = 0.71

a. What is the probability that the sample proportion is between 0.70 and 0.80? (Round intermediate calculations to 4 decimal places,

Solution

Normal Distribution
Proportion ( P ) =0.71
Standard Deviation ( )= Sqrt (P*Q /n) = 0.71*0.29/200
Normal Distribution = Z= X- u / sd ~ N(0,1)  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.7) = (0.7-0.71)/0.0321
= -0.01/0.0321 = -0.3115
= P ( Z <-0.3115) From Standard Normal Table
= 0.3777
P(X < 0.8) = (0.8-0.71)/0.0321
= 0.09/0.0321 = 2.8037
= P ( Z <2.8037) From Standard Normal Table
= 0.99747
P(0.7 < X < 0.8) = 0.99747-0.3777 = 0.6198                  

b)
              
P(X < 0.7) = (0.7-0.71)/0.0321
= -0.01/0.0321= -0.3115
= P ( Z <-0.3115) From Standard Normal Table
= 0.3777