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.
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.