CAIE: A Level - Mathematics 9709 - Probability and Statistics 1
Normal Distribution / Finding Probability by Approximation
KEYPOINTS:
Normal Distribution is written as X ~ N(μ, σ2)
Mean = μ = np
Variance = σ2 = np(1 – p)
Standard Deviation is the Square Root of Variance [S.D = \(\sqrt{Var}\)]
Standardised score z = \(\frac{x - \mu}{\sigma}\), where x is the raw score, μ is the mean and σ is the standard deviation.
Probability can be found from the Normal distribution table using z–score.
φ(z) = P(Z ≤ z), φ(-z) = 1 - φ(z)
Binomial distribution B(n, p) can be approximated by the normal distribution N(np, npq) provided both np and nq = n(1 – p) are greater than 5. When the normal distribution is used to approximate the binomial (or any other distribution that takes only integer values), a continuity correction must be used.
Past Papers Topic Wise QuestionsA Level: Mathematics 9709 - Probability and Statistics 1Normal Distribution | Finding Probability by Approximation
