Answer
$\mu=23.45$ and $22.79 \leq\mu\leq24.11$
Work Step by Step
Given $n=49, \bar X=23.45, \sigma=2.8, c=0.9$
we have $\alpha/2=0.05, Z_{\alpha/2}=1.65$
the margin of error is
$E=Z_{\alpha/2}\frac{\sigma}{\sqrt n}=1.65\times\frac{2.8}{\sqrt {49}}=0.66$
the confidence interval is $(23.45-0.66, 23.45+0.66)$ which is $(22.79,24.11)$
The point estimate of the population mean is $\mu=23.45$
The 90% confidence interval of the true mean is $22.79 \leq\mu\leq24.11$
