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
No of pupils
68
184
294
402
480
310
164
98
(a) Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution. (b) Use your curve to estimate the : (i) cut off mark, if 300 candidates are to be offered admission ; (ii) probability that a candidate picked at random, scored at least 45%.
Explanation
(a)(i)
Marks (x)
No of pupils (f)
Cum Freq
11 - 20
68
68
21 - 30
184
252
31 - 40
294
546
41 - 50
402
948
51 - 60
480
1428
61 - 70
310
1738
71 - 80
164
1902
81 - 90
98
2000
(ii) (b)(i) Cut off mark = 68 marks for reading at 1700. (ii) Candidates scoring more than 45% = 2000 - 720 = 1280 \(\therefore\) P(scoring at least 45%) = \(\frac{1280}{2000} = 0.64\)
