Question

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

Answer 1

The standard deviation for the combined assignment is 5 minutes.

To combine the standard deviations, we use:


`\sigma_z=√((\sigma_x)^2+(\sigma_y)^2)`

With our information, we have:

`\sigma_z=√(3^2+4^2) \\ \\=√(9+16)=√(25)=5`

Answer 2

5 min

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