Answer
$25.1 \leq\mu\leq 30.9$
Work Step by Step
We are given $n=5, \bar X=28, s=3, c=0.9$
for $df=n-1=4, \alpha/2=0.05$ we find $t_{\alpha/2}=2.132$
The margin of error $E=2.132\times\frac{3}{\sqrt 5}=2.9$
The confidence interval $(\bar X-E, \bar X +E)$ is $(25.1, 30.9)$
The 90% confidence interval of the true mean number of mail
carriers who are bitten by dogs each month is $25.1 \leq\mu\leq 30.9$
