Normal Approximation of Binomial (AQA A-Level Mathematics): Quizzes

$np \geq 5$ and $n(1-p) \geq 5$

To ensure Binomial is 'bell-shaped'

$\mu = np$

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

Normal is continuous, Binomial is discrete

$0.5$

$P(64.5 < X < 75.5)$

$1.20$

Yes, $np=70$ and $n(1-p)=30$, both $>5$

$0.7698$