A manufacturer produces high-precision pressure sensors. Historical quality control data indicates that 1 in 80 sensors produced has a calibration error.
In a random sample of 800 sensors, determine:
(i) the mean number of sensors with a calibration error,
(ii) the standard deviation of the number of sensors with a calibration error, giving your answer to 3 decimal places.
A quality analyst believes that, due to new maintenance protocols, the actual proportion of sensors with calibration errors is lower than the historical data suggests.
A random sample of 1200 sensors is taken and 8 are found to have a calibration error.
A test of the analyst's claim is to be carried out at the 5% level of significance.
(i) State the hypotheses for this test.
(ii) Using a suitable approximation, carry out the test.
It is further claimed that 15% of sensors with calibration errors also possess a specific micro-fracture defect.
To test this claim, a random sample of n n\,n sensors with calibration errors is inspected. The random variable Y Y\,Y represents the number of sensors in the sample that possess the micro-fracture defect.
A two-tailed test, at the 5% level of significance, is carried out to determine if the proportion differs from 15%.
The critical region for the test is Y=0Y = 0Y=0 or Y≥wY \ge wY≥w.
Find the smallest possible value of n n\,n and the corresponding value of www.
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.