A bakery produces loaves of bread whose weights, WWW grams, follow a normal distribution with mean 800 g800\text{ g}800 g and standard deviation 25 g25\text{ g}25 g.
Estimate the proportion of loaves that weigh more than 840 g840\text{ g}840 g.
The bakery classifies loaves into three categories: Small, Standard, and Large, such that there is an equal proportion of loaves (exactly 13\frac{1}{3}31) in each category.
Find the weight limits that define the 'Standard' category.
A loaf is selected at random from the 'Large' category.
Find the probability that this loaf weighs less than 830 g830\text{ g}830 g.
A customer selects a random sample of 3 loaves from the bakery's total production.
Find the probability that there is exactly one loaf from each of the three categories.
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.