RipkenB636377 RipkenB636377
  • 25-10-2022
  • Mathematics
contestada

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

Respuesta :

JahkingL328937 JahkingL328937
  • 25-10-2022

The equation that will represent this situation will be:

[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]

Thus:

[tex]\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)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]

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.

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