Question

The average reading speed of students completing a speed-reading course is 435 words per minute (wpm). If the standard deviation is 60 wpm, find the z-score associated with the following reading speeds then interpret the result. Round to two decimal places. a. 340 wpmb. 475 wpmc. 420wpmd. 610wpm

Answer 1

Answer:

a)

$Z = -1.58$

Z = -1.58 means that a reading speed of 340 wpm is 1.58 standard deviations below the mean reading speed.

b)

$Z = 0.67$

Z = 0.67 means that a reading speed of 475 wpm is 0.67 standard deviations above the mean reading speed.

c)

$Z = -0.25$

Z = -0.25 means that a reading speed of 420 wpm is 0.25 standard deviations below the mean reading speed.

d)

$Z = 2.92$

Z = 2.92 means that a reading speed of 610 wpm is 2.92 standard deviations above the mean reading speed.

Step-by-step explanation:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations a measure X is above or below the mean.

In this problem, we have that:

$\mu = 435, \sigma = 60$

a. 340 wpm

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{340 - 435}{60}$

$Z = -1.58$

Z = -1.58 means that a reading speed of 340 wpm is 1.58 standard deviations below the mean reading speed.

b. 475 wpm

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{475 - 435}{60}$

$Z = 0.67$

Z = 0.67 means that a reading speed of 475 wpm is 0.67 standard deviations above the mean reading speed.

c. 420wpm

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{420 - 435}{60}$

$Z = -0.25$

Z = -0.25 means that a reading speed of 420 wpm is 0.25 standard deviations below the mean reading speed.

d. 610wpm

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{610 - 435}{60}$

$Z = 2.92$

Z = 2.92 means that a reading speed of 610 wpm is 2.92 standard deviations above the mean reading speed.