Question

The B(225, 1/5) distribution can be approximated by what normal distribution?

N(45, 6)

N(225, 1/5)

B(45, 6)

N(225, 1/5)

N(225, 6)

Answer 1

Judging by the notation, I would presume \(B(n,p)\) is a binomial distribution of size \(n\) and success probability \(p\), while \(N(\mu,\sigma)\) is a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).

The mean of a binomial distribution can be approximated with \(np\), and the variance with \(\sqrt{np(1-p)}\).

Answer 2

Typically, though, the normal distribution is described with parameters \(\mu\) and \(\sigma^2\) (the variance). See here: http://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation

Your class/textbook must be using a different convention.

Answer 3

ty