Inverse Normal Distribution: Find a

Question

Find a such that: P(a < Z < 1.6)=0.787

Answer 1

P(a < z < 1.6) = 0.787

P(a < z < b) = P(z < b) - P(z < a), so:

P(a < z < 1.6) = P(z < 1.6) - P(z < a) = 0.9452 - P(z < a)

so substituting:

0.9452 - P(z < a) = 0.787

P(z < a) = 0.1582

Find z score corresponding to 0.1582; it is -1.002, so

a = -1.002