First, calculate the critical Z-value for the 85% confidence interval:
Z_crit = Norm.inv ( 0.925, 0, 1 ) = 1.44
The standard error for our sample will be given by sigma/sqrt(n) = 9.3/sqrt(397) = 0.467
So, the confidence interval is given by Mean +/- Z_crit x Standard error
= 18.2 +/- 1.44 x 0.467
= 17.5 (lower) and 18.9 (upper)
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