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 30.03 cm or higher. (type an integer or a decimal. do not round.) select the correct choice below and fill in the answer box(es) to complete your choice. a. the adult male foot length of 30.3 cm is not significant because it is between cm and cm. (type integers or decimals. do not round.) b. the adult male foot length of 30.3 cm is significantly low because it is less than cm. (type an integer or a decimal. do not round.) c. the adult male foot length of 30.3 cm is significantly high because it is greater than cm. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the range rule of thumb

The range rule of thumb states that the usual range of values is from $\text{mean} - 2\times\text{standard deviation}$ to $\text{mean} + 2\times\text{standard deviation}$. Values outside this range are considered significantly low or high.

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

Step2: Calculate the lower limit

Lower limit $= \text{mean} - 2\times\text{standard deviation} = 27.11 - 2\times1.46$
$= 27.11 - 2.92 = 24.19$ cm.

Step3: Calculate the upper limit

Upper limit $= \text{mean} + 2\times\text{standard deviation} = 27.11 + 2\times1.46$
$= 27.11 + 2.92 = 30.03$ cm.

Step4: Analyze the value 30.3 cm

We have the value $30.3$ cm. Now, compare it with the upper limit ($30.03$ cm). Since $30.3>30.03$, it is significantly high.

Answer:

For option A: The lower limit is $24.19$ and the upper limit is $30.03$. So we fill $24.19$ and $30.03$.

For option C: The value to fill is $30.03$ because $30.3$ is greater than $30.03$.

The correct choice is C. The adult male foot length of 30.3 cm is significantly high because it is greater than $30.03$ cm.