Answer: (36.7, 39.3)
Step-by-step explanation:
Confidence interval for population mean:
[tex]\overline{x}\pm z^c\dfrac{\sigma}{\sqrt{n}}[/tex] , where n= sample size, [tex]\overline{x}[/tex]= sample mean, [tex]\sigma[/tex] = population standard deviation, [tex]z^c[/tex] = critical z value.
Given: n= 40 , [tex]\sigma=5\ g,\ \ \ \overline{x} = 38.0\ g[/tex]
Critical z-value for 90% confidence = 1.645
Then, required confidence interval:
[tex]38.0\pm(1.645)\dfrac{5}{\sqrt{40}}\\\\= 38.0\pm (1.645)(0.79057)\\\\\approx38.0\pm1.30\\\\= (38-1.30,\ 38+1.30)=(36.7,\ 39.3)[/tex]
Hence, a 90% Confidence Interval = (36.7, 39.3)
