(15 marks) Diana's kids, Naomi and Isaac, play a lot of video games together. On a...

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level, the number of points Naomi scores has a Discrete Uniform distribution on [5,11] and the number of 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 100 games, the total number of points scored by Naomi and Isaac is at least 1600. Do not evaluate the expression.

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

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

(d) (5) Suppose Naomi and Isaac want to play until they have a 96% probability of being above a total score of 1600. What is the smallest number of games they must play to achieve this?

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orchestra answered 11 months ago

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