solution:-
mean = 90 , standard deviation = 13 , n = 4
degree of freedom df = n - 1 = 4 - 1 = 3
we look into t-distribution table with df and with 90% confidence level
critical value t = 2.353
confidence interval formula
=> mean +/- margin of error
=> mean +/- t * standard deviation/sqrt(n)
=> 90 +/- 2.353 * 13/sqrt(4)
=> 90 +/- 15.29
=> (74.71 , 105.29)
the 90% confidence interval for the population mean is (74.71 , 105.29)
the margin of error is 15.29
=> interpret the result
With 95% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.
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