An automated laboratory sensor measures the concentration CCC of a specific solution in parts per million (ppm). The readings follow a normal distribution with mean μ\muμ. For the analysis to be considered highly precise, the deviation from the mean should be strictly controlled such that the probability of a reading exceeding the mean by more than 12 ppm is exactly 0.005; that is P(C>μ+12)=0.005P(C > \mu + 12) = 0.005P(C>μ+12)=0.005.
Show that this precision requirement implies a standard deviation of 4.659 ppm, to 3 decimal places.
A quality control technician suspects the sensor is calibrated incorrectly and is over-reporting the concentration. A random sample of 10 readings is taken, yielding the following results:
253.2,250.5,256.8,251.4,253.1,250.8,255.1,257.0,248.9,255.2 253.2, 250.5, 256.8, 251.4, 253.1, 250.8, 255.1, 257.0, 248.9, 255.2 253.2,250.5,256.8,251.4,253.1,250.8,255.1,257.0,248.9,255.2Assuming the population standard deviation is 4.659 ppm, test at the 1% significance level whether the mean concentration being measured is greater than 250 ppm. State your hypotheses clearly.
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.