Normal distribution

Approximating μ as σ

68% of data is 1 σ

95% is 2σ

98% is 3σ

from the mean (3 on either side so 68% 2 σ total)

Standardised equation

Z = X-μ/σ

ϕ notation

P(Z<a) = ϕ(a)

P(Z>a) = ϕ(-a)

When can you estimate with Binomial and normal?

N is large(>50), p is close to 0.5

Formula for binomial and normal approximations

μ = np

σ = (root) np(1-p)

How to use the continuity correction

When approximating with binomial and normal distribution, either with or without equals to, always add it in

If (Y < 60), use (X<59.5)

If (Y > 60), use (X> 60.5)

Normal distribution hypothesis testing equation

Xbar ~ N(μ,σ²/n)