Converting Discrete Random Variables to Continous

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The discrete random variable H takes values 1, 2, 3 and 4.

It is given that:

The mean of a random sample of 50 observations of is denoted by .

Use a suitable approximation to find

I understand that the appropriate thing to do here is to use a normal approximation to the binomial one, N(2.5, 0.025). However, I don't understand why exactly the continuity correction applied is:

Namely the 2.59 part. I understand generally to change discrete binomial variables into continuous normal, you would have to first turn a strict inequality into an unstrict one and then extend the range of the inequality by 0.5, but I'm just a bit unsure about this specific example!