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.
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.