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%
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
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