Question

in designing a work - desk, it is found that males have sitting knee heights with a mean of 21.8 in and a standard deviation of 2.2 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.
a. what heights are significantly low? 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 less than
in
b. heights that are greater than
in
c. heights that are greater than
in and less than
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 less than
in
b. heights that are greater than
in
c. heights that are greater than
in and 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

Explanation:

Step1: Recall range - rule - of - thumb

According to the range - rule - of - thumb for significant values, 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 $\mu = 21.8$ in and $\sigma = 2.2$ in.

Step2: Calculate significant low value

The formula for significant low value is $L=\mu - 2\sigma$.
Substitute $\mu = 21.8$ and $\sigma = 2.2$ into the formula:
$L=21.8-2\times2.2=21.8 - 4.4 = 17.4$ in.

Step3: Calculate significant high value

The formula for significant high value is $H=\mu + 2\sigma$.
Substitute $\mu = 21.8$ and $\sigma = 2.2$ into the formula:
$H=21.8 + 2\times2.2=21.8+4.4 = 26.2$ in.

Step4: Determine non - significant values

Non - significant values are between $\mu - 2\sigma$ and $\mu + 2\sigma$.

Answer:

a. A. Heights that are less than $17.4$ in
b. B. Heights that are greater than $26.2$ in
c. A. Heights that are greater than $17.4$ in and less than $26.2$ in