3. Two basketball players, Steph and Klay, score baskets at random at a rate of \(2 \cdot 1\) and \(1 \cdot 9\) respectively per quarter of a game. Assume that baskets are scored independently, and that Steph and Klay each play all four quarters of the game.
- Stating the model that you are using, find the probability that they will score a combined total of exactly 20 baskets in a randomly selected game.
- A quarter of a game lasts 12 minutes.
- State the distribution of the time between baskets for Steph. Give the mean and standard deviation of this distribution.
- Given that Klay scores at the end of the third minute in a quarter of a game, find the probability that Klay doesn't score for the rest of the quarter.
- When practising, Klay misses \(4 \%\) of the free throws he takes. One week he takes 530 free throws. Calculate the probability that he misses more than 25 free throws.