Question

in designing a work - desk, it is found that males have sitting knee heights with a mean of 20.2 in. and a standard deviation of 2.4 in. (based on data from the department of transportation). use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high.

c heights that are less than 15.4 in.

b. what heights are significantly high? select the correct answer below and fill in the answer box(es) to complete your choice.
(type integers or decimals. do not round.)
a heights that are greater than in and less than in
b heights that are greater than 25 in
c heights that are less than in

c. what heights are neither significantly low nor significantly high? select the correct answer below and fill in the answer box(es) to complete your choice.
(type integers or decimals. do not round.)
a. heights that are greater than in and less than in.
b. heights that are less than in.
c. heights that are greater than in.

Explanation:

Step1: Recall range - rule - of - thumb

According to the range - rule - of - thumb, significant low values are $\mu - 2\sigma$ or lower, and significant high values are $\mu+ 2\sigma$ or higher, where $\mu$ is the mean and $\sigma$ is the standard deviation.
Given $\mu = 20.2$ in and $\sigma=2.4$ in.

Step2: Calculate significant low value

$\mu - 2\sigma=20.2-2\times2.4=20.2 - 4.8 = 15.4$ in.

Step3: Calculate significant high value

$\mu + 2\sigma=20.2+2\times2.4=20.2 + 4.8 = 25$ in.

Step4: Determine non - significant values

Values that are neither significantly low nor significantly high are between $\mu - 2\sigma$ and $\mu + 2\sigma$, i.e., between 15.4 in and 25 in.

Answer:

b. B. Heights that are greater than 25 in
c. A. Heights that are greater than 15.4 in and less than 25 in