3.4

5 34-week: z=2400-2600/660=-0.30 40-week: z=3300-3500/470=-0.43 The 40-week gestation period baby weights less relative to the gestion period

7 75-inch man: z=75-69.6/3.0=1.8 70-inch woman: z=70-64.1/3.8=1.55 The 75-inch man is relatively taller than 70-inch woman

9 Clayton Kershaw: z=1.77-3.430/0.721=-2.30 Felix Hernandez: z=2.14-3.598/0.762=-1.91 Kershaw had the better year relative to his peers because lower ERAs are better, and Kershaw had 2.30, which is lower than 1.91

11 100-meter backstroke: z=45.3-48.62/0.98=-3.39 200-meter backstroke: z=99.32-106.58/2.38=-3.05 Ryan is better in the 100-meter backstroke

13 z=x-200/26=1.5–>x=239, the minimum score to be accpeted is 239

15

  1. 15% of 3-5 month old males have head circumference at 41.0cm or less. 85% of 3-5 month old males have head circumference more than 41.0cm

  2. 90% of 2 years old females have waist circumference at 52.7cm or less. 10% of 2 years old females have waist circumference more than 52.7

  3. Except 40-49 age group, the heights at each percentile decrease when the ages increase, it could implies that males are getting higher

22

  1. (hint the mean = 10.08, standard deviation = 1.885), z=7.8-10.08/1.885=-1.21, the Blackie hemoglobin is 1.21 standard deviations below the mean

  2. q1=8.9+9.4/2=9.15 q2=9.9+10.0/2=9.95 q3=11.0+11.2/2=11.1

  3. IQR=11.1-9.15=1.95, the range of the middle 50% of the hemoglobin in cats is 1.95

  4. lower fences=9.15-1.5(1.95)=6.225 upper fences=11.1+1.5(1.95)=14.025 The outlier is 5.7 hemoglobin level

25 q1=429+437/2=433 q3=489+490/2=489.5 IQR=489.5-433=56.5 upper fences=489.5+1.5(56.5)=574.25

3.5

3

  1. Right skewed

  2. 0, 1, 3, 6, 16

4

  1. Symmetric

  2. -1, 2, 5, 8, 11

5

  1. median=40

  2. q3=52

  3. The y variable has more dispersion because it has much span of the lines and much span of the box

  4. The shape is symmetric because the horizontal lines are nearly the same and the median is near the center

  5. The shape is right skewed because the right line is longer than the left one and the median is more left to the center

6

  1. Median: 16

  2. q1=22

  3. y variable has more dispersion because the span of the lines and the span of the box is larger

  4. Yes, the outlier is about 30

  5. The shape is left shewed because the left line is longer and the median is more right to the center

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. 42, 50.5, 54.5, 57.5, 69

boxplot(dat3)

  1. The shape is symmetric because the horizontal lines are about the same and the median is near the center

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. 7.2, 9.0, 10.0, 11.2, 16.4

boxplot(dat3)

  1. The shape is right skewed because the right line is longer and the median is more to the left