3.4

5 The z-score for the 34-week gestation period baby is -0.303, and the z-score for the 40 week gestation period baby is -0.426. The 40-week gestation period baby weighs less relative to the gestation period since it is more standard deviations below the mean.

7 The z-score for the 75-inch tall man is 1.8, while the z-score for the 70-inch tall woman is 1.55. Since the man is more standard deviations above the mean, he is relatively taller than the woman.

9 Clayton Kershaw had the better year. His z-score was -2.30 while Hernandez’s z-score was -1.91. Thus, Kershaw was more standard deviations below the mean than Hernandez was.

11 Ryan is better in the 100-meter backstroke because his z-score is more negative in this race than in the 200-meter backstroke (-3.388 vs -3.050).

13 The minimum score that an applicant must make is 239.

15

  1. In order for the head circumference of a male 3-5 months of age to be greater than 15% of the individuals in the population, the circumference must be at least 41.0 cm.

  2. In order for the waist circumference of a female 2 years of age to be greater than 90% of the individuals in her population, her circumference needs to be at least 52.7 cm.

  3. The average height of a male goes down with age.

22

  1. (hint the mean = 10.08, standard deviation = 1.885), The z-score for Blackie is -1.21. This means that he is 1.21 standard deviations below the mean concentration of hemoglobin.

  2. The first quartile is 9.15, the second quartile (median) is 9.95, and the third quartile is 11.1.

  3. IQR = Q3 - Q1: 11.1 - 9.15 = 1.95. This is the range that 50% of the data falls into.

  4. The lower fence is 6.225 and the upper fence is 14.025. There is one outlier which is the cat with a concentration of 5.7.

25 The cutoff point is 574.25 minutes.

3.5

3

  1. This data is skewed to the left.

  2. Min: 0 Q1: 2 Q2: 3 Q3: 6 Max: 16

4

  1. Normal distribution

  2. Min: -1 Q1: 2 Q2: 5 Q3: 7 Max: 11

5

  1. 40

  2. 52

  3. Variable y has more dispersion because it’s whiskers extend farther out than the whiskers of variable x.

  4. The shape of the distribution of variable x is fairly normal. The box looks about equal on both sides of the median, and the whiskers seem to extend out in equal lenths in both directions.

  5. The shape of the distribution of variable y is skewed to the left since the upper fence is farther out from the median than the lower fence.

6

  1. 15

  2. 23

  3. Variable y has more dispersion because it has longer whiskers than variable x and a more wide-ranging box.

  4. Yes it has one outlier at 30.

  5. The shape of the distribution of variable y is skewed to the right since it has a longer lower whisker than the upper whisker.

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. Min: 42 Q1: 50.5 Q2: 54.5 Q3: 57.5(note data is in order) Max: 69

boxplot(dat3)

  1. The shape of the distribution is relatively normal. There doesn’t seem to be much dispersion towards the lower fence or the upper fence, both are equal.

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. Min: 7.2 Q1: 9.1 Q2: 10.0 Q3: 11.2 Max: 16.4(note data is in order)

boxplot(dat3)

  1. This graph looks skewed to the right as there is a greater dispersion of values to the left of Q1.