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Big Town Fisheries recently stocked a new lake in a city park with fish of various sizes. The distribution of the lengths of these fish

Big Town Fisheries recently stocked a new lake in a city park with fish of various sizes. The distribution of the lengths of these fish is approximately normal with a mean of 8 inches and a standard deviation of 2 inches.

  1. Find the probability that an individual fish has a length that is greater than 8.5 inches. Report your answer with four decimals places.
  2. Find the probability that the mean of a random sample of 25 fish has a length that is greater than 8.5 inches. By Central Limit Theorem, the sample means are normal with mean 8 inches and standard deviation 2/5 or 0.4. Report your answer with four decimal places.
  3. Suppose the distribution of fish lengths in this lake was non-normal but had the same mean and standard deviation. Of the two probabilities you computed in questions 1 and 2, which ones would you still be able to compute? Enter your answer as 1 or 2 or both or none.

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