A golfer believes that the distance, in metres, that she hits a ball with a 5 iron, follows a continuous uniform distribution over the interval [100, 150].
Find the median and interquartile range of the distance she hits a ball, that would be predicted by this model.
Explain why the continuous uniform distribution may not be a suitable model.
(2 marks)
The continuous random variable \(X\) has the following cumulative distribution function:
$$\mathrm { F } ( x ) = \begin{cases} 0 , & x < 0 \frac { 1 } { 64 } \left( 16 x - x ^ { 2 } \right) , & 0 \leq x \leq 8 1 , & x > 8 \end{cases}$$
Find \(\mathrm { P } ( X > 5 )\).
Find and specify fully the probability density function \(\mathrm { f } ( x )\) of \(X\).
Sketch \(\mathrm { f } ( x )\) for all values of \(x\).