Answer
$\mu=7.5$ and $7.46\leq \mu\leq 7.54$
Work Step by Step
Given $\bar X=7.5, n=1500, c=0.95, \sigma=0.8$
we have $\alpha/2=0.025, Z_{\alpha/2}=1,96$
and the margin of error is
$E=1.96\times\frac{0.8}{\sqrt {1500}}=0.04$
The confidence interval can be constructed as
(7.5-0.04, 7.5+0.04) which is (7.46, 7.54)
The point estimate of the population mean is $\mu=7.5$
The 95% confidence interval of the true mean is $7.46\leq \mu\leq 7.54$
