Adding or subtracting 0.5 from the binomial random variable x's interval endpoints (i.e., the so-called continuity correction) improves the normal approximation to the binomial by correcting for or accounting for the "missing" corners of the probability rectangles corresponding to values of x.

Continuity Correction

An adjustment made to a discrete distribution when approximating it to a continuous distribution.

Binomial Random Variable

A type of random variable that counts the number of successes in a fixed number of independent trials with the same probability of success.

Normal Approximation

A technique used to approximate discrete probability distributions with a normal distribution when certain conditions are met.