did I solve this right?

Question

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. Construct a 95% confidence interval for the population mean cost of a used car.

ii. Calculate the error bound.

iii. Explain what a “95% confidence interval” means for this study.

 

i.

mean = 6425 n = 84 and standard deviation = 3156

The 95% confidence interval for the population mean is,
=mean ± 1.96 *σ /√n
= 6425 + 1.96 * 3156 /√84

= 6425 + 147.28√21
= 6425 + 674.922

= 7099.922

 

= 6425 - 1.96 * 3156 /√84
= 6425 - 147.28√21
= 6425 - 674.922

=5750.078

 

Answer: (5750.078, 7099.922)

 

ii.

 

=EBM=Zα/2*σ/√n
EBM = 1.96 * 3156 / √84
= 674.922

 

iii.

The  95% confidence interval means that you are 95% confident that the mean lie in the interval 5750.078 and 7099.922

 

Answer 1

I didn't do the arithmetic but it Looks good.

 

Only change I would make is add the word "population" in iii: "that the population mean lies... "