Question 161795
The formula for standard error is,
{{{sqrt((p(1-p))/n)}}},
where p is the population proportion and n is sample size.
{{{sqrt((p(1-p))/n)=sqrt((p(1-p))/200)=.0337}}}
{{{(p(1-p))/200=.00113569}}}
{{{p(1-p)=.227138}}}
{{{p-p^2=.227138}}}
{{{p^2-p+.227138=0}}}
Use the quadratic formula,
{{{p = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{p = (-(-1) +- sqrt( (-1)^2-4*1*(0.227138) ))/(2*1) }}}
{{{p = (1 +- sqrt( 1-4*1*(0.227138) ))/(2*1) }}}
{{{p = (1 +- sqrt( 1-.908522) )/(2) }}}
{{{p = (1 +- sqrt( .091448) )/(2) }}}
{{{p = (1 +- .3024 )/(2) }}}
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{{{p[1] = (1 + .3024 )/(2) }}}
{{{p[1]=1.3024/2=0.6512}}}
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{{{p[2] = (1 - .3024 )/(2) }}}
{{{p[2] =.6976/2=0.3488 }}}
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The answer is  D) 0.35 or 0.65.