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?
Hi,
This is a good question!
If you have gone through past-year questions thoroughly, you will see that continuity correction is most typically applied to a single variable that has been approximated by a normal distribution. Thus, you do not need to worry about linear combinations of variables that have been approximated by normal distributions.
However, if a question on linear combination does appear (e.g. 2001 & 2003), I would suggest that you give two possibilities: the case where no continuity correction is carried out and the case where continuity correction is carried out.
Take for example, a question from N2003:
X ~ B(20, 0.4) becomes N(8, 4.8)
Y ~ B(30, 0.6) becomes N(18, 7.2)
To find P(Y - X > 13):
Case 1: No continuity correction
P(Y - X > 13) = 0.193, with GC
Case 2: With continuity correction
P(Y - X > 13) = P(Y - X >= 14) = P(Y - X > 13.5) = 0.156, with GC
Thanks!
Cheers,
Wen Shih
Hi,
Just to add that statisticians do not always agree. One classic example is the procedure for calculating quartiles. Thanks!
Cheers,
Wen Shih