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

Explanation:

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

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 $\sigma=1.9$ in.

Step2: Calculate the value for significantly low

The formula for significantly low values is $x\leq\mu - 2\sigma$. Substitute $\mu = 20.2$ and $\sigma = 1.9$ into the formula: $x\leq20.2-2\times1.9$.
$x\leq20.2 - 3.8$.
$x\leq16.4$.

Step3: Calculate the value for significantly high

The formula for significantly high values is $x\geq\mu + 2\sigma$. Substitute $\mu = 20.2$ and $\sigma = 1.9$ into the formula: $x\geq20.2+2\times1.9$.
$x\geq20.2 + 3.8$.
$x\geq24$.

Step4: Determine the non - significant values

The values that are neither significantly low nor significantly high are in the range $16.4\lt x\lt24$.

Answer:

a. B. Heights that are less than $16.4$ in.
b. Heights that are greater than or equal to $24$ in.
c. Heights that are greater than $16.4$ in. and less than $24$ in.