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.
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.