Question

a group of adult males has foot lengths with a mean of 27.11 cm and a standard deviation of 1.46 cm. use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. is the adult male foot length of 30.3 cm significantly low or significantly high? explain. significantly low values are 24.19 cm or lower. (type an integer or a decimal. do not round.) significantly high values are □ cm or higher. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the range rule of thumb

The range rule of thumb states that significantly low values are \( \text{mean} - 2\times\text{standard deviation} \) and significantly high values are \( \text{mean} + 2\times\text{standard deviation} \).

Given \( \text{mean} = 27.11 \) cm and \( \text{standard deviation} = 1.46 \) cm.

Step2: Calculate significantly high values

Significantly high values are \( \text{mean} + 2\times\text{standard deviation} \).

Substitute the values: \( 27.11 + 2\times1.46 \)

First, calculate \( 2\times1.46 = 2.92 \)

Then, \( 27.11 + 2.92 = 30.03 \)

Now, we check the value 30.3 cm. Since \( 30.3>30.03 \), we need to find the significantly high limit first (wait, the problem also asks for significantly high values limit, let's re - check the steps).

Wait, the first part: Significantly low values: \( \text{mean}-2\sigma=27.11 - 2\times1.46=27.11 - 2.92 = 24.19 \) (which matches the given value for low).

Significantly high values: \( \text{mean}+2\sigma=27.11+2\times1.46 = 27.11 + 2.92=30.03 \)

Now, the adult male foot length is 30.3 cm. Since \( 30.3>30.03 \), it is significantly high. But the question also has a blank for significantly high values limit, which we calculated as 30.03.

Answer:

Significantly high values are \( \boldsymbol{30.03} \) cm or higher.