Page 66 - 2021-bfw-SPA-4e-TE-sample.indd

Chapter 2 STATS applied! 147

Chapter 2 STATS applied! TEACHING TIP:
STATS applied!
Chapter 2 Main Points
Do you sudoku? How recently have you reminded your STATS applied!
students that not all distributions
Mr. Starnes played an online game of sudoku at www.websudoku are approximately normal? That’s
.com . He finished an easy puzzle in 3 minutes and 20 seconds.
The graph provides information about how well he did (his certainly the case with the distribution
time is marked with an arrow). The density curve shown was of completion times for easy sudoku
Jeffrey Coolidge/Photodisc/Getty Images
constructed from a histogram of times for millions of easy sudoku puzzles. If you have sufficient time, have
games played at this website. students play 1 or 2 games of sudoku.
Your time: 3 minutes, 20 seconds They can then interpret their percentile.
(C) 2021 BFW Publishers -- for review purposes only.
Also, ask students to explain why the
figure shows an arrow in the left tail
of the distribution, but states that Mr.
Starnes’s rank is the “Top 19%.” (This
should remind students that for sudoku
puzzles, smaller times are better!)
Watch carefully as your students
complete Question 5. It’s fair to compare
0 min 30 mins
Rank: Top 19% Mr. Starnes and Judy based on z-scores,
but it’s not fair for them to try to turn
1. Describe the shape of the density curve. Judy’s z-score into a percentile. We

2. Which is larger for the distribution of time to solve easy puzzles on this site: the mean or the median? don’t know if Judy’s times to complete
Explain your answer. medium puzzles is approximately
3. State and interpret the percentile for Mr. Starnes’s time of 3 minutes and 20 seconds. normal, so we don’t have any way to

4. From long experience, Mr. Starnes’s times to finish an easy sudoku puzzle at this website can be modeled convert her time into a percentile.
by a normal distribution with mean 4.2 minutes and standard deviation 0.7 minute. In what percent of the
games that he plays does the author finish an easy puzzle in less than 3 minutes and 20 seconds? ( Note: Knowing both Mr. Starnes and Judy
3 minutes and 20 seconds is not the same as 3.20 seconds!) personally, there is no doubt at all that
5. Mr. Starnes’s wife Judy, who is an avid sudoku player, completed a medium puzzle at this site in 5 minutes. Judy is the better sudoku player!
This table summarizes the mean and standard deviation of times to complete easy and medium puzzles
at this website.
Difficulty level Mean SD Answers to Chapter 2 STATS
applied!
Easy 13.5 minutes 7.9 minutes
Medium 17.9 minutes 9.2 minutes
1. skewed to the right
Whose performance is better, relatively speaking: Mr. Starnes’s 3 minutes and 20 seconds on an easy
puzzle or his wife Judy’s 5 minutes on a medium puzzle? Justify your answer. 2. mean > median because the
distribution is skewed to the right.
3. Mr. Starnes’s finishing time is at the
19th percentile of this distribution.
About 19% of players finished an easy
puzzle faster than he did.
3.33 − 4.2
4. (i) z = =−1.24
0.7
Table A: The proportion of z-scores less
than z = –1.24is0.1075.
03_StarnesSPA4e_24432_ch02_088_153.indd 147 07/09/20 1:59 PM
(ii) Tech: Applet/normalcdf(lower:–1000,
=
upper: 3.33,mean: 4.2, SD:0.7)0.1070.
In about 10.7% of games, Mr. Starnes
finishes an easy puzzle in less than
3 minutes and 20 seconds.
3.33 −13.5
5. Mr. Starnes: z = =−1.29
7.9
5 −17.9
Mr. Starnes’s wife: z = =−1.40
9.2
Mr. Starnes’s wife performed better
because her z-score was less than
Mr. Starnes’s.

CHAPTER 2 • STATS applied! 147

03_TysonTEspa4e_25177_ch02_088_153_4pp.indd 147 10/11/20 7:49 PM