A research drone measures the atmospheric pressure at a specific altitude. The pressure PPP, in suitable units, is modeled as a continuous random variable having a uniform distribution on the interval [α−3,α+9][\alpha - 3, \alpha + 9][α−3,α+9], where α\alphaα is a constant relating to the specific layer of the atmosphere. A random sample of nnn independent observations of PPP is collected, where nnn is large.
Apply the Central Limit Theorem to find an approximate distribution for the sample mean Pˉ\bar{P}Pˉ. Give your answer in terms of nnn and α\alphaα where appropriate.
The nnn observations have a sample mean of 85.585.585.5. Given that the upper limit of the 98%98\%98% confidence interval for α\alphaα is 82.732682.732682.7326,
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.