Question

question 25, *3.2.35
part 3 of 3
a group of adult males has foot lengths with a mean of 27.64 cm and a standard deviation of 1.42 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 24.5 cm significantly low or significantly high? explain.
significantly low values are 24.8 cm or lower.
(type an integer or a decimal. do not round.)
significantly high values are 30.48 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 24.5 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 24.5 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 24.5 cm is significantly high because it is greater than cm
(type an integer or a decimal. do not round.)

Explanation:

Step1: Recall range - rule - of - thumb

Significantly low values are $\mu - 2\sigma$ and significantly high values are $\mu+ 2\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 27.64$ cm and $\sigma=1.42$ cm.

Step2: Calculate significantly low value

$\mu - 2\sigma=27.64-2\times1.42=27.64 - 2.84=24.8$ cm.

Step3: Calculate significantly high value

$\mu + 2\sigma=27.64 + 2\times1.42=27.64+2.84 = 30.48$ cm.

Step4: Compare the given value

The given foot - length is $24.5$ cm. Since $24.5<24.8$, it is significantly low.

Answer:

B. The adult male foot length of 24.5 cm is significantly low because it is less than 24.8 cm.