Answer to Question #143873 in Statistics and Probability for Vladimyr Lubin

Question

The brain volumes ​(cm3​) of 20 brains have a mean of 1172.9 cm3 and a standard deviation of 129.3 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 1471.5 cm3 be significantly​ high?

Answer 1

Solution

From the range rule of thumbs, the UCL (upper control limit) and LCL (lower control limit) can be obtained using the formula:

$$\bar{x} \pm 3 \sigma$$ $$UCL = \bar{x} + 3 \sigma$$ $$=1172.9 + 3(129.3) = 1560.8$$

$$LCL= \bar{x} - 3 \sigma$$ $$=1172.9 - 3(129.3) = 785$$

A brain volume of 1471.5 cm3 is not significantly high since it falls within the control limits (i.e <1560.8 )