A deep-sea research submersible has a maximum payload capacity of 1200 kg1200\text{ kg}1200 kg.
The weights of Type A scientific crates are normally distributed with mean 110 kg110\text{ kg}110 kg and standard deviation 15 kg15\text{ kg}15 kg.
The weights of Type B scientific crates are normally distributed with mean 85 kg85\text{ kg}85 kg and standard deviation 10 kg10\text{ kg}10 kg.
Assume that the weights of individual crates are independent.
Find the probability that when 6 Type A6\text{ Type A}6 Type A crates and 5 Type B5\text{ Type B}5 Type B crates are loaded onto the submersible, the total payload exceeds 1200 kg1200\text{ kg}1200 kg.
The mission commander decides to set a limit on the total number of crates, ccc, that can be carried on a single dive. Find the largest integer value of ccc such that the probability of the total payload exceeding 1200 kg1200\text{ kg}1200 kg is less than 2%2\%2%, regardless of the combination of crate types used.
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.