Question

Use the confidence interval to find the estimated margin of error. Then find the sample mean.

Answer 1

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 :-

$\overline{x}\pm E$

or $(\overline{x}-E,\ \overline{x}+E)$

, where $\overline{x}$ = sample mean.

E = Margin of error .

The given confidence interval : (3.8,4.8 )

Lower limit : $\overline{x}-E=3.8$                (1)

Upper limit =  $\overline{x}+E=4.8$                (2)

Eliminate equation (1) from (2) , we get

$2E=1.0\\\\\Rightarrow\ E=\dfrac{1}{2}=0.5$

⇒ The estimated margin of error = 0.5 centimeter

Add (1) and (2) ,we get

$2\overline{x}-E=8.6\\\\\Rightarrow\ \overline{x}=\dfrac{8.6}{2}=4.3$  

⇒ The sample mean = 4.3 centimeters