When you use a continuous normal distribution to approximate a binomial probability, you need to move 0.5 units to the left and right of the midpoint. This is so you can include all possible x-values in the interval.
This is called a continuity correction
For instance, let's convert the following binomial to normal distribution.
The probability of getting between 200 and 250 successes, inclusive.
The discrete midpoint values are 200, 201, 202,....., 250. The interval for the
normal distribution is 199.5<x<250.5
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