Question 1183149
Let {{{X}}} represent the random variable for the nicotine content of a cigarette.


Then Chebyshev's theorem states that


{{{P(abs(X - mu) <= k*sigma) = P(abs(X - 1.52) <= 0.07k)>= 1-1/k^2}}}.


a.  Let {{{1-1/k^2 = 24/25}}}  ==> {{{k^2 = 25}}}  ===> {{{k=5}}}.

===> {{{abs(X - 1.52) <= 0.07*5 = 0.35}}}

==>  {{{-0.35 <= X - 1.52 <= 0.35}}}   <==> {{{1.17 <= X <= 1.87}}}.


b.  Apply the same procedure as in part (a), but now letting {{{1-1/k^2 = 48/49}}}, which gives {{{k = 7}}}.