Answer: (29.35, 40.95)
Step-by-step explanation:
Formula to find the confidence interval for population mean :-
[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}=35.15[/tex]
[tex]\sigma=18[/tex]
n= 37
Using z-table, the critical z-value for 95% confidence = z* = 1.96
Then, the confidence interval for the population mean will be :
[tex]35.15\pm (1.96)\dfrac{18}{\sqrt{37}}[/tex]
[tex]=35.15\pm (1.96)\dfrac{1.7}{6.08276}[/tex]
[tex]=35.15\pm (1.96)(2.95918)[/tex]
[tex]\approx35.15\pm5.80[/tex]
[tex]=(35.15-5.80,\ 35.15+5.80)=(29.35,\ 40.95)[/tex]
Hence, a 95% confidence interval for the population mean = (29.35, 40.95)
