Question

in designing a work desk, it is found that males have sitting knee heights with a mean of 22.9 in. and a standard deviation of 1.5 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 19.9 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 25.9 in.
b. heights that are less than 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:

To solve this problem, we use the range rule of thumb, which states that significant values are typically outside the range of \( \text{mean} - 2 \times \text{standard deviation} \) to \( \text{mean} + 2 \times \text{standard deviation} \). Values within this range are not significant.

Part (a): Significantly Low Heights

The range rule of thumb for significantly low values is \( \text{mean} - 2 \times \text{standard deviation} \).

Step 1: Identify the mean and standard deviation

Mean (\( \mu \)) = 22.9 in, Standard Deviation (\( \sigma \)) = 1.5 in.

Step 2: Calculate the lower bound

\[
\mu - 2\sigma = 22.9 - 2(1.5) = 22.9 - 3 = 19.9
\]

Significantly low heights are those less than 19.9 in.

Part (b): Significantly High Heights

The range rule of thumb for significantly high values is \( \text{mean} + 2 \times \text{standard deviation} \).

Step 1: Use the mean and standard deviation

Mean (\( \mu \)) = 22.9 in, Standard Deviation (\( \sigma \)) = 1.5 in.

Step 2: Calculate the upper bound

\[
\mu + 2\sigma = 22.9 + 2(1.5) = 22.9 + 3 = 25.9
\]

Significantly high heights are those greater than 25.9 in.

Part (c): Neither Significantly Low nor High

Values that are neither significantly low nor high lie between the lower and upper bounds: \( \text{mean} - 2\sigma \) to \( \text{mean} + 2\sigma \).

From parts (a) and (b), the bounds are 19.9 in (lower) and 25.9 in (upper). Thus, heights are neither significantly low nor high if they are greater than 19.9 in and less than 25.9 in.

Final Answers

a. Significantly low: Heights less than \( \boldsymbol{19.9} \) in.
b. Significantly high: Heights greater than \( \boldsymbol{25.9} \) in.
c. Neither: Heights greater than \( \boldsymbol{19.9} \) in and less than \( \boldsymbol{25.9} \) in.

Answer:

To solve this problem, we use the range rule of thumb, which states that significant values are typically outside the range of \( \text{mean} - 2 \times \text{standard deviation} \) to \( \text{mean} + 2 \times \text{standard deviation} \). Values within this range are not significant.

Part (a): Significantly Low Heights

The range rule of thumb for significantly low values is \( \text{mean} - 2 \times \text{standard deviation} \).

Step 1: Identify the mean and standard deviation

Mean (\( \mu \)) = 22.9 in, Standard Deviation (\( \sigma \)) = 1.5 in.

Step 2: Calculate the lower bound

\[
\mu - 2\sigma = 22.9 - 2(1.5) = 22.9 - 3 = 19.9
\]

Significantly low heights are those less than 19.9 in.

Part (b): Significantly High Heights

The range rule of thumb for significantly high values is \( \text{mean} + 2 \times \text{standard deviation} \).

Step 1: Use the mean and standard deviation

Mean (\( \mu \)) = 22.9 in, Standard Deviation (\( \sigma \)) = 1.5 in.

Step 2: Calculate the upper bound

\[
\mu + 2\sigma = 22.9 + 2(1.5) = 22.9 + 3 = 25.9
\]

Significantly high heights are those greater than 25.9 in.

Part (c): Neither Significantly Low nor High

Values that are neither significantly low nor high lie between the lower and upper bounds: \( \text{mean} - 2\sigma \) to \( \text{mean} + 2\sigma \).

From parts (a) and (b), the bounds are 19.9 in (lower) and 25.9 in (upper). Thus, heights are neither significantly low nor high if they are greater than 19.9 in and less than 25.9 in.

Final Answers

a. Significantly low: Heights less than \( \boldsymbol{19.9} \) in.
b. Significantly high: Heights greater than \( \boldsymbol{25.9} \) in.
c. Neither: Heights greater than \( \boldsymbol{19.9} \) in and less than \( \boldsymbol{25.9} \) in.