Question

a group of adult males has foot lengths with a mean of 27.04 cm and a standard deviation of 1.13 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 29.6 cm significantly low or significantly high? explain
significantly low values are 24.78 cm or lower
(type an integer or a decimal. do not round.)
significantly high values are 29.3 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 29.6 cm is significantly high because it is greater than □ cm.
(type an integer or a decimal. do not round.)
b. the adult male foot length of 29.6 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 29.6 cm is not significant because it is between □ cm and □ cm.
(type integers or decimals. do not round)

Explanation:

Step1: Recall the range rule of thumb

The range rule of thumb states that values are significantly low if they are less than \(\mu - 2\sigma\), significantly high if they are greater than \(\mu+ 2\sigma\), and not significant if they are between \(\mu - 2\sigma\) and \(\mu + 2\sigma\). Here, \(\mu = 27.04\) (mean) and \(\sigma=1.13\) (standard deviation).

Step2: Calculate \(\mu - 2\sigma\) and \(\mu + 2\sigma\)

For \(\mu - 2\sigma\):

$$
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$$

For \(\mu + 2\sigma\):

$$
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$$

Step3: Check the value of \(29.6\)

Since \(29.6>29.3\) (the value of \(\mu + 2\sigma\))

Answer:

A. The adult male foot length of \(29.6\) cm is significantly high because it is greater than \(29.3\) cm.