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.
