The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of 16 observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (40.04,43.96)(40.04, 43.96)(40.04,43.96).
Find the mean of the sample.
Show that the standard deviation σ\sigmaσ is 4.
The a%a \%a% confidence interval using the 16 observations has a width of 3.3.
Calculate the value of aaa.
Find the smallest sample size, of observations from XXX, that would be required to obtain a 95%95\%95% confidence interval for μ\muμ of width at most 2.5.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.