Question

during a school event, students participated in a charity walk to raise funds. the data set below shows the distance (in kilometers) that students walked:
\\{3.2, 3.5, 3.5, 3.7, 3.8, 3.9, 4.1, 4.1, 4.1, 4.3, 4.4, 4.6, 4.7, 4.8, 4.8\\}. what is the probability that students walked at least 4.4 kilometers during the charity walk?

use the geogebra spreadsheet to find the mean and standard deviation. use these values to create a normal distribution for the data set. then use the geogebra probability calculator to solve the problem.

type your answer in the box. use the \\(\sqrt{x}\\) button to enter math symbols and expressions. for decimal values, type your answer in two decimal places.

about % of the students walked at least 4.4 kilometers, with mean kilometers and standard deviation kilometers.

Explanation:

Calculate the sample mean

Using the Sample Mean knowledge point

$$
LATEXBLOCK0
$$

Calculate the sample standard deviation

Using the Sample Standard Deviation knowledge point

$$
LATEXBLOCK1
$$

Calculate the z-score for 4.4 kilometers

We find the standard score corresponding to the boundary value.

$$ z = \frac{x - \mu}{\sigma} = \frac{4.4 - 4.1}{0.5} = \frac{0.3}{0.5} = 0.6 $$

Find the normal probability

We determine the probability of a value being at least 4.4.

$$ P(X \ge 4.4) = P(Z \ge 0.6) = 1 - \Phi(0.6) \approx 1 - 0.7257 = 0.2743 $$

Converting to a percentage gives approximately \(27.43\%\).

Answer:

About <blank>27.43</blank>% of the students walked at least 4.4 kilometers during the charity walk, with mean <blank>4.1</blank> kilometers and standard deviation <blank>0.5</blank> kilometers.