Find the z scores that separate the middle 80% of the distribution from the area in the tails of the standard normal distribution

Question

Find the z score that separates 80% of the distribution 

Answer 1

This happens when P(X<-k) = 0.10 and P(X>C) = 0.10

                                                

 

 P(x<k) = 0.10  ---->   k = -1.2818

 

P(X>c) = 0.10 --->  1 - P(X<c) = 0.90 ---> -p(x<c) = -0.10 ---> p(x<c) = 0.10

  By symmetry that happens at k=1.2818