5. Suppose that my score on a computer game can be regarded as a continuous rand

Question

5. Suppose that my score on a computer game can be regarded as a continuous randonm variable following a normal distribution with mean 350 and standard deviation 45. a) Determine the value such that I score higher than this value 92.5% of the time. Also report the relevant z-score for performing this calculation. b) Determine the probability that my combined score for three independent, randomly selected games exceeds 1000. (As always, show your work.) c) Suppose that my goal is to exceed 1000 points, and I am offered the choice between playing three independent games, or playing a single game and multiplying my score by 3 Which choice provides the higher probability of exceeding 1000 points? Justify your answer with appropriate probability calculations.

Explanation / Answer

a)

z score = 1.4395 at 92.5% right of the z curve

Required value = 1.4395*45 + 350 = 414.78

b) p [xbar > 1000] = p [Z > 1000 - 1050/(45) = p [Z > -1.11] = 0.8665

c) in first case combined score of 3 independent games = 350 + 350 + 350 = 1050

in second case score is multiplied by 3 = 3* 350 = 1050

So probability of both the cases is 0.8665

Therefore both the above cases are same

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