A $95\%$ confidence interval for a mean is $110\mathrm{.}1$ to $124\mathrm{.}7.$ Is the value given a plausible value of $?$

$($a$)=120\mathrm{.}5$

$($b$)=111\mathrm{.}5$

$($c$)=99\mathrm{.}4$

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