If \(\mu=70,\sigma=10\), find z-score of \(x=85\).

Answer: \(z=\frac{85-70}{10}=1.5\).

If \(z=-0.8\), \(\mu=50,\sigma=5\), find \(x\).

Answer: \(x=50+(-0.8)(5)=46\).

In a normal model, what does \(P(Z>2)\) represent?

Answer: Area to the right of z=2 (upper-tail probability).

Why do we standardize before using z-tables?

Answer: Tables are for \(N(0,1)\), so we convert \(X\) to \(Z\).

Checkpoints