A precision automated nozzle dispenses a volume VVV ml of a chemical reagent, where VVV is modeled as a continuous random variable uniformly distributed on the interval [k−1.5,k+4.5][k - 1.5, k + 4.5][k−1.5,k+4.5], where kkk is a calibration constant.
A quality control audit takes a random sample of 80 dispensations, yielding a sample mean volume of vˉ=42.6\bar{v} = 42.6vˉ=42.6 ml.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean volume Vˉ\bar{V}Vˉ.
Hence, find a 98% confidence interval for kkk. Give the limits of your interval to 3 significant figures.
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.