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Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular...

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Diana's kids, Naomi and Isaac, play a lot of videogames together. On a particular level, the number of points Naomiscores has a Discrete Uniform distribution on [5,11] and the numberof points Isaac scores has a Discrete Uniform distribution on [6,9]. Each time they play, their scores are independent.

(a) (2) Write down an expression for the probability that in 100games, the total number of points scored by Naomi and Isaac is atleast 1600. Do not evaluate the expression.

(b) (2) Find the mean and variance of the total number of pointsscored by Naomi and Isaac in one game.

(c) (6) Using the Central Limit Theorem, find the approximateprobability in (a). You should use a continuity correction. Justifywhy the approximation is appropriate in this situation.

(d) (5) Suppose Naomi and Isaac want to play until they have a96% probability of being above a total score of 1600. What is thesmallest number of games they must play to achieve this?

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