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 □ 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. Here, the mean $\mu = 20.2$ inches and the standard deviation $\sigma=2.4$ inches.

Step2: Calculate the significant low value

We use the formula $\mu - 2\sigma$. Substitute $\mu = 20.2$ and $\sigma = 2.4$ into the formula: $20.2-2\times2.4=20.2 - 4.8=15.4$ inches.

Step3: Calculate the significant high value

We use the formula $\mu + 2\sigma$. Substitute $\mu = 20.2$ and $\sigma = 2.4$ into the formula: $20.2+2\times2.4=20.2 + 4.8 = 25$ inches.

Step4: Determine the non - significant values

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

Part (a)

The values that are significantly low are heights that are less than $15.4$ inches. So the answer for part (a) is C. Heights that are less than $15.4$ in.

Part (b)

The values that are significantly high are heights that are greater than $25$ inches.

Part (c)

The values that are neither significantly low nor significantly high are heights that are greater than $15.4$ inches and less than $25$ inches.

Answer:

a. C. Heights that are less than $15.4$ in
b. Heights that are greater than $25$ in
c. Heights that are greater than $15.4$ in and less than $25$ in