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 ____

Respuesta :

The margin of error would tell how many percentage differs from Ā 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, [tex]\mu = 76[/tex]
  • Population standard deviation, [tex]\sigma = 11[/tex]
  • Sample mean, [tex]\bar x = 80[/tex]
  • Margin of error , [tex]E = 2.3[/tex]

The range (R) is calculated as:

[tex]R = \bar x \pm E[/tex]

Substitute known values

[tex]R = 80 \pm 2.3[/tex]

Expand

[tex]R = (80 - 2.3,80 + 2.3)[/tex]

Evaluate the difference and sum

[tex]R = (77.7,82.3)[/tex]

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

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