Answer: (6.1386, 6.8614)
Step-by-step explanation:
When population standard deviation is known , then the formula to find the confidence interval for population mean is given by :-
[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean.
z*= critical z-value
n= sample size.
[tex]\sigma[/tex] = Population standard deviation.
As per given , we have
[tex]\overline{x}=6.5[/tex]
[tex]\sigma=1.7[/tex]
n= 85.
We know that, the critical z-value for 95% confidence = z* = 1.96
Then, the confidence interval for the population mean will be :
[tex]6.5\pm (1.96)\dfrac{1.7}{\sqrt{85}}[/tex]
[tex]=6.5\pm (1.96)\dfrac{1.7}{9.2195}[/tex]
[tex]=6.5\pm (1.96)(0.18439)[/tex]
[tex]\approx6.5\pm0.3614[/tex]
[tex]=(6.5-0.3614,\ 6.5+0.3614)=(6.1386,\ 6.8614)[/tex]
Hence, the confidence interval for the population mean = (6.1386, 6.8614)
