(a)
Scores (x) | Frequency (f) | \(fx\) |
1 | 2 | 2 |
2 | 5 | 10 |
3 | 13 | 39 |
4 | 11 | 44 |
5 | 9 | 45 |
6 | 10 | 60 |
| \(\sum f = 50\) | \(\sum fx = 200\) |
\(Mean (\bar{x}) = \frac{\sum fx}{\sum f} = \frac{200}{50} = 4\)
\(d = x - 4\) | \(|d|\) | f | \(f|d|\) |
-3 | 3 | 2 | 6 |
-2 | 2 | 5 | 10 |
-1 | 1 | 13 | 13 |
0 | 0 | 11 | 0 |
1 | 1 | 9 | 9 |
2 | 2 | 10 | 20 |
| | | \(\sum f|d| = 69\) |
Hence, Mean Deviation = \(\frac{\sum f|d|}{\sum f} = \frac{69}{50} \)
= \(1.38\)
(b) Let E denote the event of getting a score of at least 4.
\(n(E) = 11 + 9 + 10 = 30\)
\(p(E) = \frac{n(E)}{n(S)} = \frac{30}{50}\)
= \(0.6\)