Answer: c. 6.14 and 6.86
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z^*(\dfrac{\sigma}{\sqrt{n}})[/tex]
, where n= sample size
[tex]\overline{x}[/tex] = Sample mean
[tex]\sigma[/tex] = Population standard deviation
z*= Critical z-value.
As per given , we have
n= 85
[tex]\overline{x}=6.5[/tex]
[tex]\sigma=1.7[/tex]
For 0.95 degree of confidence interval , the critical z-value is 1.96. (By z-table).
So , the required confidence interval will be:
[tex]6.5\pm (1.96)(\dfrac{1.7}{\sqrt{85}})[/tex]
[tex]6.5\pm (1.96)(\dfrac{1.7}{ 9.21954445729})[/tex]
[tex]6.5\pm (0.3614)[/tex]
[tex]=(6.5-0.3614,\ 6.5+0.3614)=(6.1386,\ 6.8614)\approx(6.14,\ 6.86)[/tex]
Hence, the confidence interval for the population mean is c. 6.14 and 6.8 .
