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5. Jax and Jyll are playing a game of bowling. Suppose that both are seasoned players, and that Jax's bowling score (random variable X) is

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5. Jax and Jyll are playing a game of bowling. Suppose that both are seasoned players, and that Jax's bowling score (random variable X) is normally distributed with a mean of 170 and a standard deviation 5 whereas Jyll's bowling score (random variable Y) is normally distributed with a mean of 175 and standard deviation of 10. Find the probability that (a) at least one of them scores over 185 in a game. Define your event composition based on the random variables X and Y clearly and show complete solutions. (b) both Jax & Jyll score somewhere between 168 to 173. Define your event composition clearly and show complete solutions. [9 points]

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