A call centre claims that the amount of time a worker spends on each phone call can be modelled by a normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.
Using this model, find the probability that the time the worker spends on a randomly selected phone call is more than 11 minutes.
The call centre manager thinks that the mean time for each phone call is more than 8 minutes. The manager takes a random sample of 20 phone calls and finds that the average time is 8.8 minutes. Test the manager's belief at the 5% significance level. You should state your hypotheses clearly.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.