Two high-speed automated packaging lines, Line A and Line B, are used to process identical orders. The time taken by Line A to process an order, in seconds, is normally distributed with mean 12.5 and variance 0.36. The time taken by Line B to process an order, in seconds, is normally distributed with mean 13.2 and variance 0.64. Processing times for all orders and lines are independent.
Determine the probability that, for a single randomly selected order, Line B completes the packaging faster than Line A.
A factory uses these lines to process a batch of 150 orders on Line A and a separate batch of 150 orders on Line B. Both lines start simultaneously.
Calculate the probability that the total time taken by Line B to complete its batch exceeds the total time taken by Line A by more than 120 seconds.
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.