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Chapter 4: Problem 50

The average reading speed of students completing a speed-reading course is 450 words per minute (wpm). If the standard deviation is \(70 \mathrm{wpm}\), find the \(z\) score associated with each of the following reading speeds. a. \(320 \mathrm{wpm}\) c. \(420 \mathrm{wpm}\) b. 475 wpm d. 610 wpm

Short Answer

Expert verified
The z-scores for the reading speeds 320 wpm, 420 wpm, 475 wpm, and 610 wpm are -1.857, -0.429, 0.357, and 2.286 respectively.

Step by step solution

01

Calculate Z-Score for 320 wpm

Use the formula for Z-score, z = (x - mean) / standard deviation. Substituting the values; z = (320 - 450) / 70 = -1.857.
02

Calculate Z-Score for 420 wpm

Again use the formula for Z-score, z = (420 - 450) / 70 = -0.429.
03

Calculate Z-Score for 475 wpm

Use the Z-score formula z = (475 - 450) / 70 = 0.357.
04

Calculate Z-Score for 610 wpm

Finally, compute the Z-score for 610 words per minute using the formula z = (610 - 450) / 70 = 2.286.

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