Answer: (960.80,1039.20)
Step-by-step explanation:
Let X denotes a random variable that represents the life of the light bulbs produced at the factory.
As per given,
[tex]\sigma=80\\\\ n=16\\\\ \overline{x}=1000[/tex]
Critical z-value for 95% confidence interval : z* = 1.96
Confidence interval for population mean:
[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}\\\\ =1000\pm (1.96)\dfrac{80}{\sqrt{16}}\\\\=1000\pm 1.96\times\dfrac{80}{4}\\\\=1000\pm 1.96\times20\\\\=1000\pm39.2\\\\=(1000-39.2,\ 1000+39.2)\\\\=(960.80,1039.20)[/tex]
So, a 95% confidence interval estimate (CIE) of the true mean life (m) of light bulbs produced in this factory = (960.80,1039.20)
