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

A biologist reports a confidence interval of (3.8,4.8 )when estimating the mean height​ (in centimeters) of a sample of seedlings.

1 Answer

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Answer: The estimated margin of error = 0.5 centimeter

The sample mean = 4.3 centimeters

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=(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}=(8.6)/(2)=4.3

⇒ The sample mean = 4.3 centimeters

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