Question

Hannah noted the height of each student in her class and found that the mean height of the students is 56 inches, with a standard deviation of 1.2 inches. the height of one of the students, james, is 59 inches. what is the z-score for james' height?

O 3.6
O -2.5
O 2.5
O -3.6

Answer 1

To find the z-score for James' height, use the z-score formula (z = (X - μ) / σ). James' height is 2.5 standard deviations above the mean, so the correct z-score is 2.5.

Step-by-step explanation:

The question asks us to calculate the z-score for James' height, given the mean height of his class and the standard deviation. The z-score is a measure of how many standard deviations an individual data point is from the mean. To calculate the z-score, you use the formula:

z = (X - μ) / σ

Where X is the data point (James' height), μ is the mean, and σ is the standard deviation.

Using the given values:

• James' height (X) = 59 inches

• The mean height of students (μ) = 56 inches

• The standard deviation (σ) = 1.2 inches

Substituting these into the formula gives:

z = (59 - 56) / 1.2 = 3 / 1.2 = 2.5

Therefore, James' height is 2.5 standard deviations above the mean. The correct option is 2.5, which is one of the options provided. In the final part of your question, we should mention the correct option, which is 2.5, representing how many standard deviations above the mean James' height is.