Answer
Confidence interval: $4.319\lt x ̅\lt4.841$
The time to graduate with a bachelor’s degree is between 4.319 and 4.841 years, with 90% confidence.
Work Step by Step
$n=50$, so:
$d.f.=n-1=49$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.676$
(According to Table VI, for d.f. = 50 and area in right tail = 0.05. Notice that there are no available values of $t$ for d.f. = 49, but the given value of $t$ is pretty close)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=4.58-1.676\times\frac{1.10}{\sqrt {50}}=4.319$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=4.58+1.676\times\frac{1.10}{\sqrt {50}}=4.841$
