I hope this is the right place for this question, but let me know if it should go somewhere else. Here's what I'm trying to figure out

I have a dataset that looks like this:

Unit # 2018 Repair Cost

1 10,277.00

2 33,615.00

3 23,442.00

4 11,220.00

5 41,321.00

6 40,801.00

7 20,896.00

8 44,753.00

9 28,659.00

10 19,753.00

11 28,760.00

12 24,537.00

13 20,536.00

14 20,959.00

15 5,693.00

16 8,290.00

17 28,715.00

18 41,550.00

19 18,459.00

20 49,197.00

21 28,955.00

22 46,149.00

23 25,273.00

24 45,867.00

25 24,716.00

26 43,519.00

27 27,884.00

28 37,714.00

29 8,001.00

30 42,151.00

31 43,197.00

32 27,245.00

33 31,736.00

34 9,503.00

35 14,946.00

The data represents a simple random sample of 35 from a larger population of 9316 units. Based on this information, I am trying to figure out how to get an estimated total repair cost for all the units with 95% confidence intervals for the year. My initial thought was to use this data to calculate a mean repair cost for one unit in 2018 with associated confidence intervals. That I can do pretty easily. My question is, can I then just multiply that mean & upper and lower confidence limits by 9316 to get a total expected repair cost with 95% CI? Intuitively it feels like it should work, but my intuition has gotten me in trouble before in Stats. Any thoughts would be much appreciated.

Thanks so much

Mike