A logistics drone has a maximum safe takeoff weight of 125 kg125\text{ kg}125 kg.
The weights of "Standard" parcels are normally distributed with mean 5.2 kg5.2\text{ kg}5.2 kg and standard deviation 0.8 kg0.8\text{ kg}0.8 kg.
The weights of "Bulk" parcels are normally distributed with mean 14.5 kg14.5\text{ kg}14.5 kg and standard deviation 2.4 kg2.4\text{ kg}2.4 kg.
Assume that the weights of individual parcels are independent.
Determine the probability that a cargo load of 5 standard5\text{ standard}5 standard parcels and 6 bulk6\text{ bulk}6 bulk parcels exceeds the maximum safe takeoff weight.
The drone operator wants to set a maximum limit of ccc parcels. Find the largest integer value of ccc such that the probability of the total weight exceeding 125 kg125\text{ kg}125 kg is less than 5%5\%5%, regardless of the combination of Standard and Bulk parcels used.
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.