Question

The brain volumes ​(cm cubed​) of 20 brains have a mean of 1162.8 cm cubed and a standard deviation of 127.1 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 1377.0 cm cubed be significantly​ high?

Answer 1

- The limits are 908.6 cm^3 and 1417cm^3

- 1337.0cm^3 is in between the limits

Explanation:

To determine the limit by taking into account the range rule of thumb, you use the fact that the limits are given by the mean plus and minus twice the standard deviation, that is:

`\overline{x}\pm 2\sigma` (1)

`\overline{x}`: mean of brain volume = 1162.8 cm^3

σ: standard deviation = 127.1 cm^3

You replace the values of the parameters in the equation (1):

`1162.8cm^3+2(127.1cm^3)=1417cm^3\\\\1162.8cm^3-2(127.1cm^3)=908.6cm^3`

Limits = (1417 , 908.6)

The limits are 908.6 cm^3 and 1417cm^3

1337.0cm^3 is in between the limits calculated above.