The yield of a synthetic polymer SSS, measured in milligrams, is modeled by a continuous uniform distribution on the interval [c−10,c+20][c - 10, c + 20][c−10,c+20], where c c\,c is a controlled reaction constant. A large random sample of n n\,n yields is taken during a production run.
Use the Central Limit Theorem to determine an approximate distribution for the sample mean Sˉ\bar{S}Sˉ. Give the parameters of the distribution in terms of n n\,n and c c\,c where appropriate.
The sample mean of the n n\,n observations is recorded as 152.4. Given that the upper bound of a 95% confidence interval for the constant ccc, based on this sample, is 147.89,
calculate the value of nnn. Show your working 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.