- The volume of water in a bottle has a normal distribution with unknown mean, \(\mu\) millilitres, and known standard deviation, \(\sigma\) millilitres.
A random sample of 150 of the bottles of water gave a 95\% confidence interval for \(\mu\) of
(327.84, 329.76)
- Using the confidence interval given, test whether or not \(\mu = 328\)
State your hypotheses clearly and write down the significance level you have used.
A second random sample, of 200 of these bottles of water, had a mean volume of 328 millilitres.
- Calculate a 98\% confidence interval for \(\mu\) based on this second sample.
You must show all steps in your working.
(Solutions relying entirely on calculator technology are not acceptable.)
Using five different random samples of 200 of these bottles of water, five \(98 \%\) confidence intervals for \(\mu\) are to be found. - Calculate the probability that more than 3 of these intervals will contain \(\mu\)