Question

Find the​ Z-scores that separate the middle 10​% of the distribution from the area in the tails of the standard normal distribution.

Answer 1

Let the Z scores that separate the middle 10% of the distribution from the area in the tails be Z₁ and Z₂.

P(Z < Z₁) = (1 - 0.10)/2 = 0.45

Take the value of Z₁ corresponding to 0.45 from standard normal distribution table.

Z₁ = -0.126

P(Z < Z₂) = (1 + 0.10)/2 = 0.55

Take the value of Z₁ corresponding to 0.55 from standard normal distribution table.

Z₁ = 0.126

The​ Z-scores that separate the middle 10​% of the distribution from the area in the tails of the standard normal distribution are -0.126 and 0.126