Answer:
n  = 400
Step-by-step explanation:
The formula for the error in our estimate is given by:
Standard Error :  √ ( p(1-p)/ n)
Error =  SE = Zα/2  √ ( p(1-p)/ n)  where
Zα/2= critical  value for 95% confidence level = 1.96
and we know our error is 3.5 %
But we do not the sample proportion p. Then what we can do is give an estimate of p in the absence of any other information.
In this case we will use p= 0.5 which is the value that maximizes the expression for the standard error :
if p = 0.8 then SE= 0.040
 p = 0.3 then SE =0.036
 p = 0.1 then  SE = 0.030
 p = 0.5 then SE = 0.050
Substituting
3.5/100  = 1.96 x  √ (( 0.5 x 0.5 ) /n )
3.5/ (100 x 1.96 x 0.5 ) = 1/ √n
0.0357 = 1 /√n
n = 20²
n = 400
