Question

1. the average height of students is 65 inches with a standard deviation of 3 inches.

a. find the z - score for a student who is 70 inches tall.
b. interpret the result.

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
Given \(\mu = 65\), \(\sigma=3\), and \(x = 70\).

Step2: Substitute the values into the formula

Substitute \(x = 70\), \(\mu = 65\), and \(\sigma = 3\) into \(z=\frac{x-\mu}{\sigma}\).

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Step3: Interpret the z - score

A z - score of \(z\approx1.67\) means that the student's height of 70 inches is approximately \(1.67\) standard deviations above the mean height of 65 inches.

Answer:

a. The z - score is \(\frac{5}{3}\approx1.67\).
b. The student's height of 70 inches is approximately \(1.67\) standard deviations above the mean height of 65 inches.