A data scientist is investigating the duration of sessions, SSS, on a new mobile application. The underlying distribution of SSS is heavily skewed towards shorter sessions and is certainly not normal, though it possesses a finite mean μ\muμ and a finite standard deviation σ\sigmaσ. For a large random sample of nnn sessions, the scientist utilizes the Central Limit Theorem to approximate the distribution of the sample mean session duration, Sˉ\bar{S}Sˉ.
Formulate the Central Limit Theorem in this specific context, explicitly stating the parameters of the resulting distribution and all conditions that must be satisfied for this approximation to be valid.
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.