Zero-effort miss (ZEM) distance is a critical parameter for many kinds of guidance laws. For highly manoeuvring target interception, ZEM becomes a random variable with an unknown prior due to noise-corrupted measurements and unknown bounded target manoeuvres. Currently, the distribution of ZEM is usually evaluated by the method of Monte Carlo simulation. In this paper, an analytical approach is proposed under the configuration of a linear estimator with a separate mode decision-maker. The resulting ZEM estimation error is subject to a biased Gaussian distribution when taking a fixed mode decision delay of the mode decision-maker into consideration. Finally, the analytical distribution is validated by comparison with Monte Carlo simulation and some meaningful use cases are discussed. The results in this paper give an insight to the design, analysis, and performance evaluation of the guidance system.