Answer
Confidence interval: $19.73\lt x ̅\lt20.47$
Work Step by Step
We want to estimate the mean using a sample whose size is greater than 30.
$n=210$, so:
$d.f.=n-1=209$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.660$
(According to Table VI, for d.f. = 100, the closest value to 209, and area in right tail = 0.05)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=20.1-1.660\times\frac{3.2}{\sqrt {210}}=19.73$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=20.1+1.660\times\frac{3.2}{\sqrt {210}}=20.47$
