3. In an old computer game a white square representing a ball appears at random at the top of the
playing area, which is 24 cm wide, and moves down the screen. The continuous random
variable X represents the distance, in centimetres, of the dot from the left-hand edge of the
screen when it appears. The distribution of X is rectangular over the interval
(a) Find the mean and variance of X.
(b) Find P( | X − 16 | < 3).
During a single game, a player receives 12 “balls”.
(c) Find the probability that the ball appears within 3 cm of the middle of the top edge of
the playing area more than four times in a single game.