Answer to Question #203379 in Statistics and Probability for Leone Muller

Question

What z- score value represents the middle 90% of the value in a normal distribution?

Answer 1

middle 90% of the value in a normal distribution

pink area = 90% =0.90

left white area= 5%=0.05

right white area= 5%=0.05

we know that

$Z_{0.0505}=-1.64\\ and\\ Z_{0.0495}=-1.65\\ then \space average \\ Z_{0.05 \space left}=-1.645\\ so\\ Z_{0.05 \space right}=+1.645\\$

so we write

z- score value represents the middle 90% of the value in a normal distribution

-1.645 to +1.645