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Chapter 4: Problem 48

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. \(475 \mathrm{wpm}\) d. \(610 \mathrm{wpm}\)

Short Answer

Expert verified
Hence, the Z-scores for 320 wpm, 420 wpm, 475 wpm, and 610 wpm are approximately -1.86, -0.43, 0.36, and 2.29 respectively.

Step by step solution

01

Compute the Z-Score for 320 wpm

First, let's compute the Z-score for a reading speed of 320 wpm according to the formula: \(Z = \frac{(X - 渭)}{蟽}\). Plugging in 320 for 'X', 450 for '渭' (mean), and 70 for '蟽' (standard deviation), the resulting Z-score is: \(Z = \frac{(320 - 450)}{70} = -1.86 \).
02

Compute the Z-Score for 420 wpm

Using the Z-score formula, with 420 as 'X', we get \(Z = \frac{(420 - 450)}{70} = -0.43\).. This Z-score corresponds to the reading speed of 420 wpm.
03

Compute the Z-Score for 475 wpm

When 'X' is 475, the Z-score becomes \(Z = \frac{(475 - 450)}{70} = 0.36 \). This is the Z-score that corresponds to the reading speed of 475 wpm.
04

Compute the Z-Score for 610 wpm

Finally, for the reading speed of 610 wpm ('X' = 610), we compute \(Z = \frac{(610 - 450)}{70} = 2.29\). This is the Z-score corresponding to 610 wpm.

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