Question

Chris attends a fashion institute that has no on-campus housing. The distance he commutes between his home and the campus is 19 kilometera. The mean distance commuted to campus among all students at the fashion institute is 27 kilometers with a standard deviation of 7 kilometers. (a) Find the z-score of Chris's commute distance relative to the commute distances among all the students at the institute. Round your answer to two decimal places. z= (b) Fill in the blanks to interpret the z-score of Chris's commute distance. Make sure to express your answer in terms of a positive number of standard deviations. Chris's commute distance is standard deviations all students at the institute.

Answer 1

The z-score for Chris's commute distance of 19 kilometers is approximately -1.14. This indicates that his commute distance is about 1.14 standard deviations below the average commute distance of 27 kilometers for all students at the fashion institute.

Step-by-step explanation:

The question asks us to calculate the z-score for Chris's commute distance to his fashion institute and then interpret this z-score. To find the z-score, we use the formula:

z = (X - μ) / σ

Where X is the value in the dataset (Chris's commute distance), μ is the mean value of the dataset (mean commute distance for all students), and σ is the standard deviation of the dataset.

In Chris's case:

X = 19 kilometers (Chris's commute distance)

μ = 27 kilometers (mean distance commuted by all students)

σ = 7 kilometers (standard deviation of commute distances)

Now we calculate the z-score:

z = (19 km - 27 km) / 7 km = -8 / 7 ≈ -1.14

To interpret the z-score, we can say that Chris's commute distance is 1.14 standard deviations below the mean commute distance of all students at the institute.