Question

The mean on a statewide biology test was 76 with a standard deviation of 11. Harris county sampled the scores of some of its students and reported a mean of 80 with a margin of error of ± 2.3.
What is the range of reasonable means for Harris County's sample?

Range: ____ to ____

Answer 1

The margin of error would tell how many percentage differs from  Harris County's sample

The range of reasonable means for Harris County's sample is 77.7 to 82.3

How to determine the range?

The given parameters are:

• Population mean, $\mu = 76$
• Population standard deviation, $\sigma = 11$
• Sample mean, $\bar x = 80$
• Margin of error , $E = 2.3$

The range (R) is calculated as:

$R = \bar x \pm E$

Substitute known values

$R = 80 \pm 2.3$

Expand

$R = (80 - 2.3,80 + 2.3)$

Evaluate the difference and sum

$R = (77.7,82.3)$

Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3

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