A grocery delivery service claims that the time taken to complete a delivery follow a normal distribution with a mean of 40 minutes and a standard deviation of 6 minutes.
Using this model, find the probability that a randomly selected delivery takes more than 50 minutes.
A logistics manager believes that the mean delivery time is actually more than 40 minutes. The manager monitors a random sample of 36 deliveries and finds the average completion time is 42.5 minutes. Test the manager's belief at the 5% significance level. State your hypotheses clearly.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.