Answer
a. $16.6$ hours
b. $15.7\lt\mu\lt17.5$
c. $15.4\lt\mu\lt17.8$
d. the 99% confidence, see explanations below.
Work Step by Step
Given $\bar X=16.6,\sigma=2.8,n=35$,
a. The best point estimate of the population mean is the sample mean $16.6$ hours
b. At the 95% confidence, the critical z-value is $z_{\alpha/2}=1.96$ and the error can be
found as $E=1.96\times\frac{2.8}{\sqrt {35}}=0.93$ so the interval of the mean can be
found as $\bar X-E\lt\mu\lt\bar X+E$ which gives $15.7\lt\mu\lt17.5$
c. At the 99% confidence, the critical z-value is $z_{\alpha/2}=2.575$ and the error can be
found as $E=2.575\times\frac{2.8}{\sqrt {35}}=1.22$ so the interval of the mean can be
found as $\bar X-E\lt\mu\lt\bar X+E$ which gives $15.4\lt\mu\lt17.8$
d. The interval for the 99% confidence is larger because a higher confidence level requires a higher critical z-value and larger error tolerance.