Yearly rainfall in a local watershed has µ = 21.2 in, σ = 3.7 in. What is the probability that a randomly selected year has a rainfall of less than 20 in? What are the mean and standard deviation for a sampling distribution of the mean for samples of size n = 36? Does the Central Limit Theorem apply?  Explain in 1 – 2 complete sentences. Find the probability that the mean of a sample of n = 36 years is less than 20 in. Would it be unlikely to select a sample of n = 36 years with a mean less than 20 in?  Use P(A) < 0.05

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Yearly rainfall in a local watershed has µ = 21.2 in, σ = 3.7 in.

  1. What is the probability that a randomly selected year has a rainfall of less than 20 in?
  2. What are the mean and standard deviation for a sampling distribution of the mean for samples of size n = 36?
  3. Does the Central Limit Theorem apply?  Explain in 1 – 2 complete sentences.
  4. Find the probability that the mean of a sample of n = 36 years is less than 20 in.
  5. Would it be unlikely to select a sample of n = 36 years with a mean less than 20 in?  Use P(A) < 0.05.
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