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Given a population with mean μ=100 and variance σ2=81, the Central Limit Theorem applies when the...

Given a population with mean μ=100 and variance σ2=81, the Central Limit Theorem applies when the sample size n≥30. A random sample of size n=30 is obtained.

  1. What are the mean, the variance, and the standard deviation of the sampling distribution for the sample mean?
  2. Describe the probability distribution of the sample mean and draw the graph of this probability distribution with its mean and standard deviation.
  3. What is the probability that x<101.5?
  4. What is the probability that x>102?
  5. What is the probability that 98<x<101?

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