Answer: [tex](\$524.22,\ \$635.78)[/tex]
Step-by-step explanation:
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.
[tex]\sigma[/tex] = Population standard deviation.
n= Sample size.
Let x be the denotes the monthly rent for unfurnished one bedroom apartments available for rent in this community.
As per given , we have
n= 10
[tex]\overline{x}=\$580[/tex]
[tex]\sigma=\$90[/tex]
Critical value for 95% confidence : z* = 1.96
So the 95% confidence interval becomes,
[tex]580\pm (1.96) \dfrac{90}{\sqrt{10}}[/tex]
[tex]=580\pm (1.96) \dfrac{90}{3.162278}[/tex]
[tex]=580\pm (1.96)(28.46)[/tex]
[tex]=580\pm 55.78[/tex]
[tex]=(580-55.78,\ 580+55.78)=(524.22,\ 635.78)[/tex]
Hence, a 95% confidence interval for the mean monthly rent for unfurnished one bedroom apartments available for rent in this community= [tex](\$524.22,\ \$635.78)[/tex]
