a. The table shows the scores of 2000 candidates in an entrance examination into a private secondary school.
% mark
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81-90
Number of pupils
68
184
294
402
480
310
164
98
Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.
bi. Use the curve to estimate the cut-off mark if 300 candidates are to be offered admission.
bii. Use your curve to estimate the probability that a candidate picked at random scored at least 45%
Verified Correct Answer: .
Step-by-Step Mathematical Solution
a.
x
f
cum. frequency
End point
11-20
68
68
20.5
21-30
184
252
30.5
31-40
294
546
40.5
41-50
402
948
50.5
50-60
480
1428
60.5
61-70
310
1738
70.5
71-80
164
1902
80.5
81-90
94
2000
90.5
bi. Cut-off mark = 64%
ii. Pr(student scoring at least 45%) = \(\frac{1075}{2000}\) = 0.5375
Source: Myschool Past Questions Archive (Record #76110)