If you approximate a binomial or Poisson
distribution, whichever the case might be, with a normal
distribution, as a rule of thumb, you have to do continuity
correction to get an accurate result.
Suppose I have a binomial random variable X which I
approximated by a normal distribution.
Similarly, I have another binomial random variable,
Y which I also approximate by another normal
distribution. Both discrete X and Y
distribution must satisfy the condition:
n>50, np>5,nq>5
Now, the random variable (X+Y) can be approximated
by a normal distribution, if X and Y are
independent.
If I want the random variable X+Y to be greater than
8, we use continuity correction to get a more accurate answer. As a
rule of thumb, the probability of (X+Y)>8 would be
P(X+Y>8.5)
But I am not sure if it would be accurate for cases
such as (10X+10Y)>85 or (10X+8Y)>76 because the random
variables have been multiplied by number.
My question is, as a rule of thumb, do you do
continuity correction for such cases, eg:
(10X+10Y)>85.5 or
(10X+8Y)>76.5?