When I was reading "cracking the GRE mathematics subject test" 4th edition page 282, there is a formula regarding approximation of binomial distribution:
In X ~ Binomial(n, p), when n is large, we could use normal distribution to approximate it.
P($a_1$ < X < $a_2$) $\approx$ $\phi$($\dfrac{a_2 - \mu + 0.5}{\sigma}$) - $\phi$($\dfrac{a_1 - \mu - 0.5}{\sigma}$)
I was quite confused about the 0.5 in RHS, I believe the formula should be:
P($a_1$ < X < $a_2$) $\approx$ $\phi$($\dfrac{a_2 - \mu}{\sigma}$) - $\phi$($\dfrac{a_1 - \mu}{\sigma}$)
I am not sure if I am correct. Any comments or help would be greatly appreciated!