The weights of bags of sugar, WWW grams, are normally distributed such that W∼N(μ,1.22)W \sim \text{N}(\mu, 1.2^2)W∼N(μ,1.22).
Given that 25%25\%25% of the bags weigh more than 502502502 grams, find the value of μ\muμ to the nearest 0.10.10.1 g.
An employee selects 151515 bags at random.
Find the probability that fewer than 222 of these bags weigh more than 502502502 grams.
A wholesaler selects 200200200 bags at random.
Using a suitable approximation, find the probability that more than 555555 of these bags weigh more than 502502502 grams.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.