AP Statistics
HW 6 - Percentiles and Z-scores
Name_________________________________
1. A student took two national aptitude tests in the course of applying for admission to colleges. The SAT the
national average is 1026 with a standard deviation of 209 points. The ACT has a national average of 20.8
with a standard deviation of 4.8 points. If the student made a 1010 on the SAT and a 19 on the ACT, on
which exam did the student perform better? Show your work to support your answer.
2. If you scored at the 90th percentile on the SAT, how would you interpret this to your little brother?
3. The average 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 wpm
b. 475 wpm
c. 420 wpm
d. 610 wpm
4. In the midnight flight, the average time was 5.4 minutes with a standard deviation of 1.2 minutes. The
average time for the Reindeer Run is 5.6 minutes with a standard deviation of 1.19 minutes. If Sally ran the
midnight flight in 5.6 minutes and her friend Beth ran the Reindeer Run in 5.7 minutes, who performed
better?
5. Is a positive z-score always better?
6. Interpret a z-score of -2.
7. The average height of an adult male is 68 inches with a standard deviation of 1.78 inches and the average
height of an adult female is 64 inches with a standard deviation of 1.64 inches. If Mary is 66 inches tall and
Ted is 69 inches tall, who is taller relative to their gender?
8. The average reaction time to a stimulus is 6 sec with a standard deviation of 1.2 second. The reaction time
to a second stimulus is 3.6 sec with a standard deviation of 0.8 seconds. If your reaction time is 4.2 sec for
the first stimulus and 1.8 sec for the second stimulus, to which stimulus are you reacting relatively more
quickly?