Solve the Problem $$\sqrt { \frac { N - n } { N - 1 } }$$

Solve the problem.
-When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the following finite population correction factor: $$\sqrt { \frac { N - n } { N - 1 } }$$
Find the $95 \%$ confidence interval for the mean of 200 weights if a sample of 35 of those weights yields a mean of $\mathrm { lb }$ and $\mathrm { a }$ standard deviation of $23.2 \mathrm { lb }$ .

A) $140.3 \mathrm { lb } < \mu < 152.3 \mathrm { lb }$
B) $138.6 \mathrm { lb } < \mu < 154.0 \mathrm { lb }$
C) $137.9 \mathrm { lb } < \mu < 154.7 \mathrm { lb }$
D) $139.3 \mathrm { lb } < \mu < 153.3 \mathrm { lb }$ .3