let-xbinnpxsimtextbinnp-using-the-normal-approximation-with-continuity-correctio

Question

Let X∼Bin(n,p)X\sim	ext{Bin}(n,p). Using the normal approximation with continuity correction, which expression should be used to approximate P(X5)P(X?

Accepted Answer

Φ(4.5−npnp(1−p))\displaystyle \Phi\left(\frac{4.5-np}{\sqrt{np(1-p)}}\right)

Answer

Φ(5−npnp(1−p)){\displaystyle\Phi\left(\frac{5-np}{\sqrt{np(1-p)}}\right)}

Answer

Φ(5.5−npnp(1−p))\displaystyle \Phi\left(\frac{5.5-np}{\sqrt{np(1-p)}}\right)

Answer

1−Φ(4.5−npnp(1−p))\displaystyle 1-\Phi\left(\frac{4.5-np}{\sqrt{np(1-p)}}\right)

Let X∼Bin(n,p)X\(\sim\)\(\text{Bin}\)(n,p). Using the normal approximation with continuity correction, which expression should be used to approximate P(X<5)P(X<5)?

Let $X \sim Bin (n, p)$ . Using the normal approximation with continuity correction, which expression should be used to approximate $P of open paren X is less than 5 close paren$ ?