1. Find each of the following.
a. \( Z \) if \( X=36, \mu=40 \) and \( \sigma=6 \)
b. \( X \) if \( \mu=1.3, z=1.5 \) and \( \sigma=0.6 \)

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Answer

b. \(X = \mu + z\cdot\sigma = 1.3 + 1.5\cdot 0.6 = 1.3 + 0.9 = 2.2\)

Steps

Step 1 ：\(Z = \frac{X-\mu}{\sigma}\)

Step 2 ：a. \(Z = \frac{36-40}{6} = \frac{-4}{6} = -\frac{2}{3}\)

Step 3 ：b. \(X = \mu + z\cdot\sigma = 1.3 + 1.5\cdot 0.6 = 1.3 + 0.9 = 2.2\)