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.
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.