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

a)

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

c)

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 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 and standard deviation , the zscore of a measure X is given by:

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

In this problem, we have that:

a. 340 wpm

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

c. 420wpm

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

d. 610wpm

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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)