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In a bowling "frame", between 0 and 10 pins might be knocked over by a bowling ball. Suppose that a particular bowling alley attracts a mixture of beginners and experts, such that we can assume that the probability mass function (pmf) of the number of pins knocked over per frame is roughly symmetric. Further, suppose that the pmf has a mean of 5.7 pins and standard deviation of 1.9 pins, and that the results of all frames are independent.

A person attends the bowling alley one evening, and bowls 31 frames. What would be the probability that they knocked over more than 200 pins?

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closed as unclear what you're asking by kjetil b halvorsen, Juho Kokkala, Michael Chernick, whuber Jan 13 at 19:19

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    $\begingroup$ Mean and standard deviation of what? After all, if you bowl 35 pins, the mean is 35 and the standard deviation is zero! $\endgroup$ – whuber Jan 11 at 17:57
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    $\begingroup$ In addition, what does "bowl 35 pins" even mean? I've heard of bowling frames but not by pins. $\endgroup$ – StatsStudent Jan 11 at 19:24
  • $\begingroup$ I meant to say 35 frames, not pins. $\endgroup$ – Abby Liu Jan 11 at 22:20
  • $\begingroup$ Okay. But it still looks like you don't have the information needed to answer this question, because it doesn't tell you anything at all about the results that would be achieved by a beginner or by an expert: it only gives you the gross "mixture" of the two. Any individual is not going to be a "mixture" of beginner and expert--presumably, they will be one or the other. You're stuck. $\endgroup$ – whuber Jan 12 at 19:43
  • $\begingroup$ Hmm I see what you mean! Let me clarify the inquiry! $\endgroup$ – Abby Liu Jan 13 at 1:18

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