Stats Solutions

[See Solution] A random variable X is normally distributed with μ=20 and σ=4. Compute z_1=(X_1-μ)/(σ) for x_1=17 . Compute Z_2=(x_2-μ)/(σ)

Question: A random variable \(\mathrm{X}\) is normally distributed with \(\mu=20\) and \(\sigma=4\).

  1. Compute \(z_{1}=\frac{X_{1}-\mu}{\sigma}\) for \(x_{1}=17 .\)
  2. Compute \(Z_{2}=\frac{x_{2}-\mu}{\sigma}\) for \(x_{2}=23\).
  3. The area under the normal curve between \(\mathrm{x}_{1}=17\) and \(\mathrm{x}_{2}=23\) is $0.547$. What is the area between \(Z_{1}\) and \(Z_{2}\) ?

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