A service elevator has a maximum load capacity of 900 kg900\text{ kg}900 kg.
The weights of adult males are normally distributed with mean 82 kg82\text{ kg}82 kg and standard deviation 12 kg12\text{ kg}12 kg.
The weights of adult females are normally distributed with mean 68 kg68\text{ kg}68 kg and standard deviation 8 kg8\text{ kg}8 kg.
Assume that the weights of individual people are independent.
Find the probability that when 7 males7\text{ males}7 males and 4 females4\text{ females}4 females are in the elevator, the total load exceeds 900 kg900\text{ kg}900 kg.
The elevator displays a sign stating: "Maximum occupancy is ccc persons."
Find the largest integer value of ccc such that the probability of the total load exceeding 900 kg900\text{ kg}900 kg is less than 1%1\%1%, regardless of the gender distribution of the occupants.
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.