Question

in designing a work desk, it is found that males have sitting knee heights with a mean of 21.9 in and a standard deviation of 1.7 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.
b. heights that are less than 18.5 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.

Explanation:

Step1: Recall range - rule - of - thumb

The 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 $\mu = 21.9$ in and $\sigma=1.7$ in.

Step2: Calculate significantly low value

We use the formula $\mu - 2\sigma$.
$21.9-2\times1.7=21.9 - 3.4=18.5$ in. So, significantly low values are less than 18.5 in.

Step3: Calculate significantly high value

We use the formula $\mu + 2\sigma$.
$21.9+2\times1.7=21.9 + 3.4 = 25.3$ in. So, significantly high values are greater than 25.3 in.

Answer:

a. B. Heights that are less than 18.5 in.
b. B. Heights that are greater than 25.3 in.