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 □ 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 to determine significantly low and high values. The mean (\(\mu\)) is 22.9 in, and the standard deviation (\(\sigma\)) is 1.5 in.

Part (a): Significantly Low Heights

The range rule of thumb states that values are significantly low if they are less than \(\mu - 2\sigma\).

Step 1: Calculate \(\mu - 2\sigma\)

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

Step 2: Simplify the expression

\[
22.9 - 3 = 19.9
\]

Thus, heights less than 19.9 in are significantly low. The correct option is C. Heights that are less than 19.9 in.

Part (b): Significantly High Heights

The range rule of thumb states that values are significantly high if they are greater than \(\mu + 2\sigma\).

Step 1: Calculate \(\mu + 2\sigma\)

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

Step 2: Simplify the expression

\[
22.9 + 3 = 25.9
\]

Thus, heights greater than 25.9 in are significantly high. The correct option is A. Heights that are greater than 25.9 in.

Part (c): Neither Significantly Low nor High

Values that are neither significantly low nor high lie between \(\mu - 2\sigma\) and \(\mu + 2\sigma\) (i.e., between 19.9 in and 25.9 in).

Answer:

s:
a. \(\boldsymbol{\text{C. Heights that are less than 19.9 in.}}\)
b. \(\boldsymbol{\text{A. Heights that are greater than 25.9 in.}}\)
c. Heights that are greater than 19.9 in. and less than 25.9 in.