The brain volumes (cm3) of 20 brains have a mean of 1094.9 cm3 and a standard deviation of 128.9 cm3. 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 1392.7 cm3 be significantly high?

Yes, a brain volume of is significantly high.

Step-by-step explanation:

Given

The range rule of thumb indicates that the usual values are within 2 standard deviations from the mean:

minimum usual value = mean - 2 * standard deviation =

maximum usual value = mean + 2 * standard deviation =

We can see that is not between and , which indicates that this value is unusually high.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)