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A fourth-grade teacher gives homework every night in both mathematics and language arts. the time to complete the mathematics homework has a mean of 10 minutes and a standard deviation of 3 minutes. the time to complete the language arts assignment has a mean of 12 minutes and a standard deviation of 4 minutes. assuming the times to complete homework assignments in math and language arts are independent, the standard deviation of the time required to complete the entire homework assignment is

Respuesta :

The standard deviation for the combined assignment is 5 minutes.

To combine the standard deviations, we use:

[tex]\sigma_z=\sqrt{(\sigma_x)^2+(\sigma_y)^2}[/tex]

With our information, we have:
[tex]\sigma_z=\sqrt{3^2+4^2} \\ \\=\sqrt{9+16}=\sqrt{25}=5[/tex]
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Answer:

5 min

Step-by-step explanation:

The combine standard deviation, SDf, of two independent variables having standard deviation, SD1 and SD2, is given by:

SDf² = SD1² + SD2²

SDf²= 3² + 4²

SDf= 5

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