Approximations with the Normal Distribution Topic Review summary

Key learning points

• Binomial → Normal when $n$ large and $p$ not too extreme; use $\\mu=np$, $\\sigma^2=npq$.
• Poisson → Normal when $\\lambda$ large; $\\mu=\\lambda$, $\\sigma^2=\\lambda$.
• Continuity correction: $P(X\\le k)\\approx P(Y<k+0.5)$ for discrete $X$.
• Standardise to $Z$ after applying the correction.
• State the approximation being used in your working.

Worked example 1 — CC

$P(X\\le 10)$ with continuity correction.

Working

$Y$ continuous approximating $X$.

Worked example 2 — Binomial params

$B(100,0.4)$ Normal params.

Working

$\\mu=np$, $\\sigma^2=npq$.

Worked example 3 — Binomial → Normal when n large and p not t

Binomial → Normal when $n$ large and $p$ not too extreme; use $\\\\mu=np$, $\\\\sigma^2=npq$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Poisson → Normal when \\\\lambda large; \\

Poisson → Normal when $\\\\lambda$ large; $\\\\mu=\\\\lambda$, $\\\\sigma^2=\\\\lambda$.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.