The time, in seconds, taken for a automated process to complete is normally distributed with a mean of 120 seconds and a standard deviation of 10 seconds. An engineer monitors a process run.
Find the probability that the process takes longer than 110 seconds.
The process has already been running for 110 seconds. Find the probability that it runs for another 20 seconds.
The engineer believes that the mean completion time for these processes is longer than 120 seconds. She records a random sample of 25 process runs and found that their mean time was 122 seconds. Stating your hypotheses clearly and using a 5% level of significance, test the engineer's belief.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.