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 5Number Summary for the heights of the
choir members: Min, 1^{st},
2^{nd}
and 3^{rd}
Quartiles and Max.
b) Find the 39^{th}
percentile and 65^{th}
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 → 33^{rd}
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 → 51^{st}
position → a
=
66in; P( X <
a)
= 0.65
→ a
=
68in.
c) P(X < 68in) = 86/130 = 66.1^{th} percentile; P(X < 71in) = 110/130 = 84.6^{th} percentile.