Question

The brain volumes ​(cm^3​) of 50 brains vary from a low of 914 cm^3 to a high of 1492 cm^3. Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 186.4 cm^3​, assuming the estimate is accurate if it is within 15 cm^3.

Answer 1

`X= 19.6 cm3`

Therefore

X is not Accurate as it Falls outside of the Volume 15cm^3

Explanation:

From the question we are told that:

Sample size
`n=50`

Volume Range
`\triangle V= 914 cm^3 to 1492cm^3`

Exact standard deviation
`\sigma_E 186.4 cm^3​,`

Generally the equation for range rule of thumb is mathematically given by

Where

`\triangle V=1492cm^3- 914 cm^3`

`\triangle V=578cm^2`

Therefore

Estimate Standard deviation

`\sigma_e=(578)/(4)`

`\sigma_e=144.5cm^3`

Since

Exact standard deviation is 186.4 cm^3​

Comparing

`X=\sigma_E- \sigma_e`

`X= ( 164.1-144.5 ) cm3`

`X= 19.6 cm3`

Therefore

X is not Accurate as is Falls outside of the Hallmark 15cm^3