Question

A coin tossed 900 times . Calculate the standard normal variate for the number of heads between 435 and 465

Answer 1

$n=900$

$p=0.5$

$\mu =np=900\times0.5=450$

$\sigma=\sqrt{np(1-p)}=\sqrt{450(1-0.5)}=15$

$P(435<X<465)=\Phi(\frac{465-450}{15})-\Phi(\frac{435-450}{15})$

$P(435<X<465)=\Phi(1)-\Phi(-1)$

$P(435<X<465)=\Phi(1)-(1-\Phi(1))$

$P(435<X<465)=\Phi(1)-1+\Phi(1)$

$P(435<X<465)=2\Phi(1)-1$

$P(435<X<465)=2(0.8413)-1$

$P(435<X<465)=1.6826-1$

$P(435<X<465)=0.6826$