The brain volumes (cm cubed) of 20 brains have a mean of 1105.1 cm cubed and a standard deviation of 123.5 cm cubed. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1332.1 cm cubed be significantly high? Significantly low values are 858 cm cubed or lower. (Type an integer or a decimal. Do not round.)

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07-02-2020
Mathematics

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The brain volumes (cm cubed) of 20 brains have a mean of 1105.1 cm cubed and a standard deviation of 123.5 cm cubed. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1332.1 cm cubed be significantly high? Significantly low values are 858 cm cubed or lower. (Type an integer or a decimal. Do not round.)

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franciscocruz28 franciscocruz28 · Answer 1 · 2020-02-07T10:24:55+01:00

Answer:

[tex]1332.1 \:cm^3[/tex] is neither significantly low nor significantly high.

Step-by-step explanation:

From the information given, we know that:

The mean is [tex]\bar{x}=1105.1 \:cm^{3}[/tex] and the standard deviation is [tex]\sigma=123.5 \:cm^{3}[/tex].

The range rule of thumb says that:

[tex]minimum \:usual \:value=\bar{x}-2\sigma\\\\maximum \:usual \:value=\bar{x}+2\sigma[/tex]

Applying these definitions, we get that

[tex]minimum \:usual \:value=1105.1-2(123.5)=858.1 \:cm^3\\\\maximum \:usual \:value=1105.1+2(123.5)=1352.1 \:cm^3[/tex]

We note that [tex]1332.1 \:cm^3[/tex] is between [tex]858.1 \:cm^3[/tex] and [tex]1352.1 \:cm^3[/tex], which indicates [tex]1332.1 \:cm^3[/tex] is neither significantly low nor significantly high.