Question

in designing a work desk, it is found that males have sitting knee heights with a mean of 21.6 in. and a standard deviation of 1.6 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.

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.)
o a. heights that are greater than □ in. and less than □ in.
o b. heights that are greater than □ in.
o c. heights that are less than □ in.

Explanation:

Step1: Recall the range rule of thumb

The range rule of thumb states that values are significantly low if they are \( \mu - 2\sigma\) or lower, significantly high if they are \( \mu+ 2\sigma\) or higher, and neither significantly low nor high if they are between \( \mu - 2\sigma\) and \( \mu + 2\sigma\). Given \( \mu = 21.6\) in and \( \sigma=1.6\) in.

Step2: Calculate the significantly low value

$$ \mu - 2\sigma=21.6-2\times1.6=21.6 - 3.2 = 18.4 $$

Step3: Calculate the significantly high value

$$ \mu + 2\sigma=21.6+2\times1.6=21.6 + 3.2=24.8 $$

Answer:

a. Significantly low: Heights that are less than \(18.4\) in.
b. Significantly high: Heights that are greater than \(24.8\) in. (Option B for part b)
c. Neither significantly low nor high: Heights that are greater than \(18.4\) in. and less than \(24.8\) in. (Option B for part a (assuming part a is about neither low nor high, but based on the problem structure, for part b the answer is as above))