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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.