Question
There are 40 players in a clay pigeon shooting club who take part in a local tournament. The scores obtained after the first round of shootings are shown in the following table.
| Score | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2 | 7 | 12 | 10 | 6 | 3 |
(a) One of the players is chosen at random. Find the probability that this player’s score was 3 or more.
(b) Calculate the mean score.
Answer/Explanation
Ans:
(a) We have
\(p(3 or more)= \frac{10+6+3}{40}=\frac{19}{40}\)
= 0.475
(b) Using the mean formula, we get
\(\bar{x}=\left [ \sum_{i=1}^{6} f_{i}x_{i}\right ]/\left [ \sum_{i=1}^{6} f_{i}\right ]\)
\(=\frac{(2)(0)+(7)(1)+(12)(2)+(10)(3)+(6)(4)+(3)(5)}{40}\)
=2.5
Question
The following table shows the amount of fuel (y litres) used by a car to travel certain distances (x km).
| Distance travelled (x km) | 14 | 35 | 80 | 115 | 145 | 170 |
| Fuel used (y litres) | 2.5 | 6.2 | 10.8 | 13.6 | 15.4 | 19.7 |
(a) Find the correlation cofficient.
The data can be modelled by the regression line with equation y = ax + b
(b) Write down the value of a and the value of b.
Answer/Explanation
Ans:
(a) r ≈ 0.991 [by using G.D.C.]
(b) a ≈ 0.101 and b ≈ 1.96 [by using G.D.C.]
(c) Evaluating y = 0.101x + 1.96 for x = 55, we get
y = 0.101(55) + 1.96
≈ 7.52 litres