Question

III

Homework Section 3-3 (A)
Question 5 of 10 (1 point) Question Attempt: 1 of 5
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Carmen attends a fashion Institute that has no on-campus housing. The mean distance commuted to cam
with a standard deviation of 9 kilometers. The distance Carmen commutes is 22 kilometers.
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Find the z-score of Carmen's commute distance relative to the commute distances among all the students
places.

Answer 1

To find the z-score of Carmen's commute distance, subtract the mean from her commute distance and divide by the standard deviation. Her z-score is approximately 0.78, meaning her commute is 0.78 standard deviations longer than the average.

Step-by-step explanation:

The z-score is a statistical measure that tells us how many standard deviations an element is from the mean of the distribution. To calculate the z-score for Carmen's commute distance, we use the formula:

Z = (X - μ) / σ

Where X is Carmen's commute distance, μ (mu) is the mean of the commute distances, and σ (sigma) is the standard deviation. Given that the mean commute distance is 15 kilometers and the standard deviation is 9 kilometers, and Carmen's commute distance is 22 kilometers:

Z = (22 - 15) / 9
Z = 7 / 9
Z = 0.78

So the z-score of Carmen's commute distance is approximately 0.78. This means Carmen's commute is 0.78 standard deviations longer than the average commute.