14E - Approximating the binomial distribution
In Section 12, it was mentioned that the normal distribution could be used to approximate the binomial distribution.
- Provided \(n\) is sufficiently large and \(p\) is not too close to \(0\) or \(1\), the binomial distribution is remarkably symmetric. Therefore, it is approximately normal in its distribution.
- Importantly, \(\mu\) and \(\sigma\) for the binomial distribution agree with those of the normal approximation.
■ If \(X\)~\(Bi(n,p)\), then the distribution can be approximated as \(X\)~\(N(np,np(1-p))\).
For the normal approximation to be suitable:
- \(n\) must be sufficiently large. As a general rule, \(n\geq 30\).
- \(p\) cannot be too close to \(0\) or \(1\). As a general rule, \(np\) and \(np(1-p)\) should both be greater than \(5\).
14E - Example 1: Approximating the binomial distribution using the normal distribution
A company imports 1800 fridges. It is known that 6% of fridges are defective in some way.
|
14E - Example 1: Video solution
Video solution coming soon! (a) \(X\)~\(N(108,101.52)\) (b) \(Pr(X<100)=0.2136\) (c) \(Pr(X<100)=0.2006\) 14E - Example 1: Practice
Question 1: ABC 14E - Example 1: Solutions
Question 1: ABC |