Answer
a. 7.2
b. $6.6\lt\mu\lt7.8$
c. $6.4\lt\mu\lt8.0$
d. the 99% confidence, see explanations below.
Work Step by Step
Given $\bar X=7.2, \sigma=2.1,n=50$,
a. The best point estimate of the population mean is the sample mean 7.2
b. At the 95% confidence, the critical z-value is $z_{\alpha/2}=1.96$ and the error can be
found as $E=1.96×\frac{2.1}{\sqrt {50}}=0.58$ so the interval of the mean can be
found as $\bar X−E\lt\mu\lt\bar X+E$ which gives $6.6\lt\mu\lt7.8$
c. At the 99% confidence, the critical z-value is $z_{\alpha/2}=2.575$ and the error can be
found as $E=2.575\times\frac{2.1}{\sqrt {50}}=0.76$ so the interval of the mean can be
found as $\bar X−E\lt\mu\lt\bar X+E$ which gives $6.4\lt\mu\lt8.0$
d. The interval for the 99% confidence is larger because a higher confidence level requires a higher critical z-value and a larger error tolerance.