A chemical dispenser in a laboratory is checked for accuracy. The random variable XXX, in millilitres, represents the actual volume of liquid dispensed when the device is set to 25.00 ml. It is known that X∼N(μ,0.122)X \sim N(\mu, 0.12^2)X∼N(μ,0.122).
Six random measurements gave the following values of xxx:
24.88,25.04,24.95,24.91,24.82,25.06 24.88, \quad 25.04, \quad 24.95, \quad 24.91, \quad 24.82, \quad 25.06 24.88,25.04,24.95,24.91,24.82,25.06(i) Calculate a 95% confidence interval for μ\muμ, giving your limits to 2 decimal places.
(ii) Based on this interval, comment on whether the dispenser is likely to be accurate.
In a separate series of nnn tests, a sample mean of 24.94 ml was obtained. A 98% confidence interval for μ\muμ resulted in an upper limit that was less than 25.00 ml. Find the minimum value of nnn.
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.