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 39th
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)
= 0.65
→ a
=
68in.
c) P(X < 68in) = 86/130 = 66.1th percentile; P(X < 71in) = 110/130 = 84.6th percentile.