STAT 200 WEEK 5 QUESTIONS

Hello Everyone, I have a hard time figuring out this question. Please help!

112. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.
(I was a little bit confused with this question. when they said standard deviation of 3156. I understood as sample standard deviation.please correct me if I am wrong).
a.Which distribution should you use for this problem? Explain your choice.
-use student’s t table. because we do not know population standard deviation (not sure if this is right)
b.Construct a 95% confidence interval for the population mean cost of a used car.
State the confidence interval.
N=84 sample mean = 6435 sample standard deviation =3156
CL=0.95 1-0.95=0.05 0.05/2=0.025 1-0.025=0.975
df =84-1=83 look up t table,value is 1.989 EBM=1.989 (3156/ square root of 84)=684.908
6425 – 684.908 =5740.092
6425 + 684.908 = 7109.908
CI (5740.092, 7109.908)
c.Explain what a “95% confidence interval” means for this study.
-We estimate with 95% confidence that the true population mean used car sales costs is between 5740.092 and 7109.908 (not quite sure if the sentence is right)

Thank you in advance!