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.
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 greater than in. and less than in.
b. heights that are greater than in.
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 in.
c. heights that are less than in.

Explanation:

Step1: Recall range - rule - of - thumb for significant values

Significantly low values are $\mu - 2\sigma$ or lower, and significantly 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 significantly low value

$\mu - 2\sigma=20.2-2\times2.4=20.2 - 4.8 = 15.4$ in. So, values less than 15.4 in are significantly low.

Step3: Calculate significantly high value

$\mu + 2\sigma=20.2+2\times2.4=20.2 + 4.8=25$ in. So, values greater than 25 in are significantly high.

Step4: Determine non - significant values

Values between 15.4 in and 25 in are neither significantly low nor significantly high.

Answer:

a. C. Heights that are less than 15.4 in.
b. B. Heights that are greater than 25 in.