Answer :
Answer: The estimated margin of error = 0.5 centimeter
The sample mean = 4.3 centimeters
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm E[/tex]
or [tex](\overline{x}-E,\ \overline{x}+E)[/tex]
, where [tex]\overline{x}[/tex] = sample mean.
E = Margin of error .
The given confidence interval : (3.8,4.8 )
Lower limit : [tex]\overline{x}-E=3.8[/tex] (1)
Upper limit = [tex]\overline{x}+E=4.8[/tex] (2)
Eliminate equation (1) from (2) , we get
[tex]2E=1.0\\\\\Rightarrow\ E=\dfrac{1}{2}=0.5[/tex]
⇒ The estimated margin of error = 0.5 centimeter
Add (1) and (2) ,we get
[tex]2\overline{x}-E=8.6\\\\\Rightarrow\ \overline{x}=\dfrac{8.6}{2}=4.3[/tex]
⇒ The sample mean = 4.3 centimeters