The table shows the marks scored by some candidates in an examination.
Marks (%)
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Frequency
7
11
17
20
29
34
30
25
21
6
(a) Construct a cumulative frequency table for the distribution and draw a cumulative frequency curve.
(b) Use the curve to estimate, correct to one decimal place, the :
(i) Lowest mark for distinction if 5% of the candidates passed with distinction ; (ii) probability of selecting a candidate who scored at most 45%.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
Marks
(%)
frequency
(f)
Cumulative
frequency
Upper class
boundaries
0 - 9
7
7
9.5
10 - 19
11
18
19.5
20 - 29
17
35
29.5
30 - 39
20
55
39.5
40 - 49
29
84
49.5
50 - 59
34
118
59.5
60 - 69
30
148
69.5
70 - 79
25
173
79.5
80 - 89
21
194
89.5
90 - 99
6
200
99.5
(b) (i) If 5% of the candidates passed the examination, then (100 - 5)% = 95% passed with a mark \(\leq\) the lowest mark for distinction.
\(\text{95% of 200} = \frac{95}{100} \times 200 \)
= 190 candidates. From the ogive, 190 corresponds to 79.5 + 8 = 87.5 marks (to one decimal place)
(ii) From the ogive, the number of candidates who scored at most 45% is 69. Hence, the probability of selecting a candidate who scored at most 45%
= \(\frac{69}{200} = 0.345 \approxeq 0.3\) (1 d.p)
Source: Myschool Past Questions Archive (Record #52579)