9/ 06/2014 The table below gives the distribution of the heights (in inches) of 130 members of a choir.


Height (in)

Frequency

Height (in)

Frequency

60

2

69

8

61

6

70

11

62

9

71

8

63

7

72

9

64

5

73

4

65

20

74

2

66

18

75

4

67

7

76

1

68

12



a) Use the table to find the 5-Number Summary for the heights of the choir members: Min, 1st, 2nd and 3rd Quartiles and Max.
b) Find the 39
th percentile and 65th percentile of heights.
c) Find the percentile that a choir members 68in tall corresponds to.


Scroll down for the solution.








9/06/2014 Solution.
a) P(X < Q1) = 0.25 → we need the height in the 25% of 130 = 32.5 → 33rd position → Q1 = 65in; likewise, P(X < Q3) = 0.75 → Q3 = 70in. Find Q2 by yourselves.
b) P(X
< a) = 0.39 → w e need the height in the 39% of 130 = 50.7 → 51st position → a = 66in; P( X < a) = 0.65a = 68in.

c) P(X < 68in) = 86/130 = 66.1th percentile; P(X < 71in) = 110/130 = 84.6th percentile.