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

Answer:

$X= 19.6 cm3$

Therefore

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

Step-by-step 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

$\sigma_e=\frac{578}{4}$

$\sigma_e=144.5cm^3$

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