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

[4, 28].

(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.