[Step-by-Step] Given a normal distribution with μ=102 and σ=15, and given you select a sample of n=9, complete parts (a) through (d). What is the probability


Question: Given a normal distribution with \(\mu=102\) and \(\sigma=15\), and given you select a sample of \(\mathrm{n}=9\), complete parts (a) through (d).

  1. What is the probability that \(\bar{X}\) is less than 95 ?
  2. What is the probability that \(\bar{X}\) is between 95 and 97.5?
  3. What is the probability that \(\bar{X}\) is above 102.8?
  4. There is a \(63 \%\) chance that \(\bar{X}\) is above what value?

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