SOA sample #27

I don't understand the solution. Maybe I missed it in ASM or something but I have no conceptual understanding of the solution. Can somebody please help me understand?

Quote:

You are given: (i) X_partial = pure premium calculated from partially credible data (ii) μ = E(X_partial) (iii) Fluctuations are limited to ±kμ of the mean with probability P (iv) Z = credibility factor Which of the following is equal to P? correct answer choice: Pr[μ - kμ <= Z(X_partial) + (1-Z)μ <= μ +kμ ]

Solution:

Quote:

The absolute difference of the credibility estimate from its expected value is to be less than or equal to kμ (with probability P). That is, |[Z(X_partial) + (1-Z)M] - [Zμ + (1-Z)M]| <= kμ -kμ <= Z(X_partial) - Zμ <= kμ Adding μ to all three sides produces answer choice (E).

SOA sample #27