Question

The mean reading speed of students completing a speed-reading course is 450 words per minute (wpm). If the standard deviation is 70 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

The z-scores associated with each reading speed are: a. -1.857, c. -0.429, b. 0.357, d. 2.286

Step-by-step solution

Understand Z-score formula

The formula to calculate the z-score is \( z = \frac{x - μ}{σ} \) where \( x \) is the value for which the z-score is being calculated, \( μ \) is the mean of the distribution, and \( σ \) is the standard deviation.

Identify Mean and Standard Deviation

From the problem, the mean reading speed (\(μ\)) is given as 450 wpm and the standard deviation (\(σ\)) is 70 wpm.

Calculate Z-scores

Plugging the values into the Z-score formula, we can calculate the z-scores: \[a. \( z = \frac{320 - 450}{70} = -1.857 \)c. \( z = \frac{420 - 450}{70} = -0.429 \)b. \( z = \frac{475 - 450}{70} = 0.357 \)d. \( z = \frac{610 - 450}{70} = 2.286 \)\]