Question

Find the Z-score for which 5% of the distributions area lies between-z and z

Answer 1

The equation that will represent this situation will be:

`\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}`

Thus:

`\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=(1.05)/(2) \\ P(x\le z)=0.525 \end{gathered}`

If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.

Answer: z-score is 0.063.