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.
