Answer: A. (636.9, 653.1)
Step-by-step explanation:
Given : Sample size : n=56
Significance level :[tex]\alpha: 1-0.95=0.05[/tex]
Critical value :[tex]z_{0.05}=1.96[/tex]
Sample mean : [tex]\overline{x}=645\text{ hours}[/tex]
Standard deviation : [tex]\sigma= 31\text{ hours}[/tex]
The 95% confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm (1.96)\dfrac{31}{\sqrt{56}}\\\\=645\pm8.1\\\\=(636.9, 653.1) [/tex]
Hence, 95% confidence interval for population mean is (636.9, 653.1).
