Answer
$119.95\lt\mu\lt123.35$
Work Step by Step
Given $n=36,\bar X=121.6,\sigma=6.36$,
As $n\gt30$, use normal distribution and at a 90% confidence the critical z-value is $z_{\alpha/2}=1.65 $
and the margin of error can be found as $E=z_{\alpha/2}\times\frac{\sigma}{\sqrt n}=1.65\times6.36/\sqrt {36}=1.75$,
thus, the best point estimate and the 90% confidence interval of the true mean is
$\bar X-E\lt\mu\lt\bar X+E$ which gives $119.95\lt\mu\lt123.35$
