A random sample of $10$ health maintenance organizations $($HMOs$)$ was selected. For each HMO, the co$-$payment $($in dollars$)$ for a doctor's office visit was recorded. The results are as follows.

$51,36,39,50,25,43,57,41,43,34$

Under the assumption that co$-$payment amounts are normally distributed, find a $95\%$ confidence interval for the mean co$-$payment amount in dollars. Give the lower limit and upper limit of the $95\%$ confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. $($If necessary, consult a list of formulas.$)$

Lower limit: $\_\_\_\_$

Upper limit: $\_\_\_\_$