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.

c. heights that are greater than
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 25.3 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.
b. heights that are less 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. Values between $\mu - 2\sigma$ and $\mu + 2\sigma$ are neither significantly low nor significantly high. Given $\mu = 21.9$ in and $\sigma=1.7$ in.

Step2: Calculate significantly low values

$\mu - 2\sigma=21.9-2\times1.7=21.9 - 3.4 = 18.5$ in.

Step3: Calculate significantly high values

$\mu + 2\sigma=21.9+2\times1.7=21.9 + 3.4 = 25.3$ in.

Step4: Determine non - significant values

Values between $18.5$ in and $25.3$ in are neither significantly low nor significantly high.

Answer:

a. Significantly low values are heights that are less than $18.5$ in.
b. Significantly high values are heights that are greater than $25.3$ in.
c. Heights that are greater than $18.5$ in and less than $25.3$ in are neither significantly low nor significantly high.