Question

For a normal distribution,

a. What z-score separates the highest 10% from the rest of the scores?
b. What z-score separates the highest 30% from the rest of the scores?
c. What z-score separates the lowest 40% from the rest of the scores?
d. What z-score separates the lowest 20% from the rest of the scores?

Answer 1

1.282, -0.5244,...

Explanation:

We know that Z is a standard normal variate with mean =0, and std dev =1

a) z-score separates the highest 10% from the rest of the scores

= 90th percentile = 1.282

b) z-score separates the lowest 30% from the rest of the scores

= 30th percentile = -0.5244

c) z-score separates the lowest 40% from the rest of the scores

= 40th percentile = -0.2533

d) z-score separates the lowest 20% from the rest of the score

=20th percentile = -0.8416