3.4

5 type answer

z score for 34-week baby = (2400-2600)/660 = -0.30 z score for 40-week baby = (3300-3500)/470 = -0.43

7 type answer

z score for a 75-inch man = (75-69.6)/3 = 1.8 z score for a 70-inch woman = (70-64.1)/3.8 = 1.55 Since 1.8 is greater than 1.55, the 75-inch man is relatively taller.

9 type answer

z score for Clayton Kershaw = (1.77-3.43)/0.721 = -2.302 z score for Felix Hernandez = (2.14-3.598)/0.762 = -1.913 Therefore Felix Hernandez had the better year.

11 type answer

z score in 100-meter backstroke= (45.3-48.62)/0.98 = -3.39 z score in 200-meter backstroke= (99.32-106.58)/2.38 = -3.05 therefore, Ryan is better at the 200-meter race.

13 type answer

minimum score= 1.5*26+200=239

15

  1. type answers

85% of males whose ages are between 3 to 5 months have head circumference longer than 41.0cm

  1. type answers

10% of females who is 2 years old have waist circumference longer than 52.7cm

  1. type answers

Only 25% of males whose ages are between 20 and 29 are taller than 181.4 cm

22

  1. (hint the mean = 10.08, standard deviation = 1.885), type answer

z score = (7.8-10.88)/1.885 = -1.634

  1. type answer

Q1=9.15 Q2= 9.95 Q3= 11.1

  1. type answer

IQR=Q3-Q1=1.95

  1. type answer

lower fence= 9.15-1.51.95=6.575 upper fence= 11.1+1.51.95=14.025

25 type answer

Q2=466 Q3=489.5 Q1=433 IQR=56.5 Upper fence=489.5+1.5*56.5=574.25

3.5

3

a)skewed to the right

b)minimum=0; maximum=15; Q1=2; Q2=3; Q3=6

4

a)normally distributed

b)minimum=-1; maximum=11; Q1=2; Q2=5; Q3=8

5

a)40

b)50

c)y has more dispersion, because it has larger range and IQR

d)x is bell-shaped, because its two whisker of the same lengh.

e)y is skewed to the right, because its whisker on the right is longer than the left one.

6

a)15

b)22

c)y has more dispersion because its IQR is larger than X’s.

d)it has one outlier=29

e)y is left-skewed, because its left whisker is longer than the one on the right.

7

dat1 <- c(60,68,77,89,98)

boxplot(dat1)

8

dat2 <- c(110,140,157,173,205)

boxplot(dat2)

9

dat3 <- c(42,43,46,46,47,
         47,48,49,49,50,
         50,51,51,51,51,
         52,52,54,54,54,
         54,54,55,55,55,
         55,56,56,56,57,
         57,57,57,58,60,
         61,61,61,62,64,
         64,65,68,69)
  1. type answer (note data is in order)

Maximum=69; minimum=42; Q1=50.5; Q2=54.5; Q3=57.5

boxplot(dat3)

  1. type answer

It is skewed to the right.

10

dat3 <- c(7.2, 7.8, 7.8, 7.9, 8.1, 8.3,
          8.5, 8.6, 8.6, 8.6, 8.7, 8.8,
          9.0, 9.1, 9.2, 9.2, 9.2, 9.4,
          9.4, 9.6, 9.7, 9.7, 9.9, 9.9,
          10.0, 10.0, 10.0, 10.1, 10.2, 10.3,
          10.0, 10.3, 10.3, 10.7, 10.7, 10.9,
          11.2, 11.2, 11.2, 11.3, 11.3, 11.3,
          11.5, 11.5, 11.7, 12.4, 12.5, 13.6,
          13.8, 14.4, 16.4)
  1. type answer (note data is in order)

Maximum=16.4; minimum=7.2; Q1=9.0; Q2=10.0; Q3=11.2

boxplot(dat3)

  1. type answer

It is right-skewed.