Suppose that we have a population proportion P = 0.20 and a random sample of size n = 100 drawn from the population. Complete (a) through (c) below. Click the icon to view the standard normal table of...

Given
1)
Population proportion P = 0.2 ; sample size n = 100
a. Probability that sample proportion is greater than 0.19 is
 
 
 
 
 
ˆ ˆ ˆ0.19
ˆ 0.19
ˆ ˆ
p E p E p
P p P
Var p Var p
  
   
 
 
-----(1)
 ˆ 0.2E p P  ;  
0.2*0.8
ˆ 0.04
100
PQ
Var p
n
  
Substitute the above values in the (1)
 
 
 
 
 
 
 
ˆ ˆ ˆ0.19
ˆ 0.19
ˆ ˆ
0.19 0.2
0.25
0.04
1 0.25 1 0.4013 0.5987
p E p E p
P p P
Var p Var p
P z P z
P z
  
   
 
 
 
     
 
      
b) Probability that sample proportion is less than 0.15 is
 
 
 
 
 
 
ˆ ˆ ˆ0.15
ˆ 0.15
ˆ ˆ
0.15 0.2
1.25 0.1057
0.04
p E p E p
P p P
Var p Var p
P z P...