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138 CHAPTER 2 • Modeling One-Variable Quantitative Data

17. (i) z = (9 9.12)/0.05 =−2.40 medical attention. What percent of adults have a (d) Compare your answers to parts (a) and (b). Does it
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and z = (9.1 9.12)/0.05 =−0.40; diastolic BP that is classified as a hypertensive crisis? make sense for the lid manufacturer to try to make one
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0.3446 – 0.0082 = 0.3364. 17. Enough chips Refer to Exercise 9. What percent of of these values larger than the other? Why or why not?
(ii) Applet/normalcdf(lower:9,upper: 9.1, pg 135 9-ounce bags of this brand of potato chips weigh 24. Bottling soda A bottling company fills bottles
between 9 and 9.1 ounces?
labeled “2 liters” with delicious lemonade. Of
=
mean:9.12, SD:0.05) 0.3364. About 18. Hey batter! Refer to Exercise 10. What percent of course, there is some variation from the target vol-
33.64% of 9-ounce bags of this brand players have batting averages between 0.250 and ume. In fact, the distribution of volume is approx-
imately normal with a mean of 2.04 liters and a
of potato chips weigh between 9 and 0.300? standard deviation of 0.03 liter.
9.1 ounces. 19. SAT scores in the middle Refer to Exercise 11. What (a) About what percent of bottles are underfilled (i.e.,
proportion of students earned scores between 500
less than 2 liters)?
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18. (i) z = (0.250.261)/0.034 =−0.32 and 600 on the SAT math test? (b) About what percent of bottles have a volume
−
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and z = (0.3 0.261)/0.034 1.15; 20. Very high BP Refer to Exercise 12. A diastolic blood greater than 2.10 liters?
pressure between 80 and 90 indicates borderline
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0.8749 – 0.37450.5004. high blood pressure. What proportion of adults have (c) About what percent of bottles are within 0.05 liter of
the target volume (i.e., between 1.95 and 2.05 liters)?
=−0.40; BFW Publishers -- for review purposes only.
borderline high blood pressure?
(ii) Applet/normalcdf(lower:0.25, (d) Based on your answers to parts (a), (b), and (c), do
you think this bottling company needs to adjust its
upper: 0.3, mean:0.261,SD: 0.034) = Applying the Concepts filling machine? Why or why not?
0.5012. About 50.1% of MLB players have 21. Watch the salt! A study investigated about 3000 meals
batting averages between 0.250 and 0.300. ordered from Chipotle restaurants using the online Extending the Concepts
site Grubhub. Researchers calculated the sodium con-
25. Backwards normal calculations A quantitative variable
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19. (i) z = (500 528)/117 =−0.24 and tent (in milligrams) for each order based on Chipotle’s can be modeled by a normal distribution with mean
published nutrition information. The distribution of
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=
z = (600 528)/117 0.62; the proportion sodium content is approximately normal with mean 50 and standard deviation 6. What value is at the 80th
percentile of the distribution? Explain your reasoning.
of z-scores between =z –0.24and 2000 mg and standard deviation 500 mg. 20
=
z = 0.62is 0.7324 –0.4052 0.3272. (a) What proportion of the meals ordered exceeded the Recycle and Review
recommended daily allowance of 2400 mg of sodium?
(ii) Applet/normalcdf(lower: 500, (b) What percent of the meals ordered had between 26. Are body weights normal? (2.4) The heights of peo-
ple of the same sex and similar ages follow normal
=
upper: 600,mean: 528,SD:117)0.3254. 1200 mg and 1800 mg of sodium? distributions reasonably closely. How about body
The proportion who earned scores 22. Egg weights In the United States, egg sizes are set by weights? The weights of women aged 20 to 29 have
the Department of Agriculture. A “large” egg, for
mean 141.7 pounds and median 133.2 pounds.
between 500 and 600 on the SAT math example, weighs between 57 and 64 grams. Sup- The first and third quartiles are 118.3 pounds and
test is approximately 0.3254. pose the weights of eggs produced by hens owned 157.3 pounds. Is it reasonable to believe that the
by a particular farmer are approximately normally
distribution of body weights for women aged 20 to
−
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20. (i) z = (80 70)/200.50 and distributed with a mean of 55.8 grams and a stan- 29 is approximately normal? Explain your answer.
dard deviation of 7.5 grams.
=
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z = (90 70)/201.00; the proportion (a) What proportion of these eggs weigh less than 50 27. Who plays video games? (1.2) The Pew Research Cen-
ter asked a random sample of 1996 U.S. adults if they
of z-scores between z = 0.50 and grams? play video games. In the sample, 165 identified them-
=
z =1.00 is 0.8413–0.6915 0.1498. (b) What percent of these eggs would be classified as selves as “gamers,” 760 said they play video games but
don’t identify as a gamer, and 1071 said they do not
“large”?
21
(ii) Applet/normalcdf(lower:80, upper: 90, 23. Put a lid on it! At fast-food restaurants, the lids for play video games. Here is a graph of these data.
=
mean:70, SD:20) 0.1499. The drink cups are made with a small amount of flex- 1200
1100
proportion who have borderline high ibility, so they can be stretched across the mouth 1000
of the cup and then snugly secured. When lids are
blood pressure is approximately 0.1499. too small or too large, customers can get frustrated, 900
800
especially if they end up spilling their drinks. At 700
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21. (a) (i) z = (2400 2000)/500 0.80; one restaurant, large drink cups require lids with Frequency 600
=
the proportion of z-scores greater than a diameter of between 3.95 and 4.05 inches. The 500
restaurant’s lid supplier claims that the diameter
400
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z = 0.80is1–0.7881 0.2119. of the large lids follows a normal distribution with 300
mean 3.98 inches and standard deviation 0.02 200
(ii) Applet/normalcdf(lower:2400,upper: inches. Assume that the supplier’s claim is true. 100 Gamer Play some Don’t play
10000,mean: 2000,SD: 500)0.2119. (a) What percent of large lids are too small to fit? Video game player status
=
The proportion of meals ordered that (b) What percent of large lids are too big to fit? (a) Explain what is potentially deceptive about this graph.
exceeded the recommended daily (c) What percent of large lids have diameters between (b) Make a bar chart for these data that isn’t deceptive.
3.95 and 4.05 inches?
allowance of 2400 mg of sodium is
approximately 0.2119.
(b) (i) z = (1200 2000)/500 =−1.60
(C) 2021
−
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and z = (1800 2000)/500 of z-scores between z = 0.16 and z =1.09 About 0.02% of lids are too big. (c) 100% − 07/09/20 1:57 PM
03_StarnesSPA4e_24432_ch02_088_153.indd 138
the proportion of z-scores is0.8621–0.5636 0.2985. 6.68% – 0.02% = 93.3% of large lids have
=
between =z –1.60and = –0.40 is (ii) Applet/normalcdf(lower:57, upper: 64, diameters between 3.95 and 4.05 inches.
z
0.3446–0.05480.2898. mean: 55.8, SD:7.5)0.2993. About 29.93% (d) It makes sense to err by making lids too
=
=
(ii) Applet/normalcdf(lower:1200,upper: of eggs would be classified as “large” (weight small rather than too large. If a lid is too small,
1800,mean: 2000,SD: 500) = 0.2898. between 57 and 64 grams). the consumer will realize it and select a new
About 28.98% of meals ordered had 23. (a) (i) z = (3.953.98)/0.02 =−1.50; lid. If the lid is too large, the consumer may
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between 1200 and 1800 mg of sodium. the proportion of z-scores less than z = –1.50 not realize it and may spill their drink.
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22. (a) (i) z = (50 55.8)/7.5 =−0.77; the is 0.0668. 24. (a) (i) z = (2 2.04)/0.03 =−1.33; the
proportion of z-scores less than z = –0.77 (ii) Applet/normalcdf(lower:–1000, proportion of z-scores less than z = –1.33 is
is 0.2206. upper: 3.95,mean: 3.98,SD: 0.02)0.0668. 0.0918.
=
(ii) Applet/normalcdf(lower:–1000, About 6.68% of the lids are too small. (ii) Applet/normalcdf(lower:–1000,
=
=
upper: 50,mean: 55.8, SD:7.5)0.2197. (b) (i) z = (4.053.98)/0.023.50; the upper: 2, mean:2.04, SD:0.03) 0.0912.
=
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The proportion of these eggs that weigh proportion of z-scores greater than z = 3.50 is About 9.1% of the bottles are underfilled
less than 50 grams is 0.22. less than 0.0002. (less than 2 liters).
=
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(b) (i) z = (57 55.8)/7.5 0.16 and
−
=
z = (64 55.8)/7.5 1.09; the proportion (ii) Applet/normalcdf(lower:4.05,
upper:1000,mean: 3.98,SD: 0.02) =0.0002.
138 CHAPTER 2 • Modeling One-Variable Quantitative Data
03_TysonTEspa4e_25177_ch02_088_153_4pp.indd 138 10/11/20 7:48 PM