Respuesta :
Answer:
a)
[tex]Z = -1.58[/tex]
Z = -1.58 means that a reading speed of 340 wpm is 1.58 standard deviations below the mean reading speed.
b)
[tex]Z = 0.67[/tex]
Z = 0.67 means that a reading speed of 475 wpm is 0.67 standard deviations above the mean reading speed.
c)
[tex]Z = -0.25[/tex]
Z = -0.25 means that a reading speed of 420 wpm is 0.25 standard deviations below the mean reading speed.
d)
[tex]Z = 2.92[/tex]
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations a measure X is above or below the mean.
In this problem, we have that:
[tex]\mu = 435, \sigma = 60[/tex]
a. 340 wpm
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{340 - 435}{60}[/tex]
[tex]Z = -1.58[/tex]
Z = -1.58 means that a reading speed of 340 wpm is 1.58 standard deviations below the mean reading speed.
b. 475 wpm
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{475 - 435}{60}[/tex]
[tex]Z = 0.67[/tex]
Z = 0.67 means that a reading speed of 475 wpm is 0.67 standard deviations above the mean reading speed.
c. 420wpm
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{420 - 435}{60}[/tex]
[tex]Z = -0.25[/tex]
Z = -0.25 means that a reading speed of 420 wpm is 0.25 standard deviations below the mean reading speed.
d. 610wpm
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{610 - 435}{60}[/tex]
[tex]Z = 2.92[/tex]
Z = 2.92 means that a reading speed of 610 wpm is 2.92 standard deviations above the mean reading speed.
