Question 1081891
Plug p = 0.2 into the first inequality and solve for n


{{{n*p > 5}}}


{{{n*0.2 > 5}}}


{{{(n*0.2)/0.2 > 5/0.2}}}


{{{n > 25}}}


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For the second inequality plug q = 1-p in first, then plug in p = 0.2, and solve for n


{{{n*q > 5}}}


{{{n*(1-p) > 5}}}


{{{n*(1-0.2) > 5}}}


{{{n*0.8 > 5}}}


{{{(n*0.8)/0.8 > 5/0.8}}}


{{{n > 6.25}}}


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Intersecting the two inequalities {{{n > 25}}} and {{{n > 6.25}}} leads to just {{{n > 25}}}, as this is the region they both share in common


So overall, the solution is {{{n > 25}}} where n is a positive whole number.


We'll need n to be larger than 25 in order to use a normal approximation.


<font size=4 color=red>The min sample size needed is 26</font>