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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.