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Because we don't know the standard deviation population, we can utilise a student's t distribution. The probability distribution is $t83.$

The average cost of an 84-year-old automobile is $\overline{X}$.

i. Using the $T I-83$ calculator, calculate the confidence interval.

Calculators TI-83, TI-83+, TI-84, TI-84+

Make a list of the information.

Press the STAT button and arrow $鈫�$button to TESTS.

Now, Arrow $鈫�$to $8:$T Interval.

Press ENTER button also.

Arrow to $鈫�$and then press ENTER.

Arrow $鈫�$and the name of the list in which the data is kept.

Enter Freq : 1 Enter $\mathit{C}$- Level : $.9$

Arrow $鈫�$to Calculate and press Enter.

The confidence interval's output,

$CI=(5740.1,7109.9)$

ii. The graph is as follows:

iii. The error bound is calculated from the formula,

$EBM=t_{n-1}\left(\frac{a}{2}\right)\frac{s}{\sqrt{n}}$

$EBM=t_{84-1}\left(\frac{0.05}{2}\right)\frac{3156}{\sqrt{84}}$

$EBM=665.0178$

If we sampled $n=84$many times, we would expect to see that$95\%$ of the time, the genuine population mean selling price of a used car would be found.