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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.