Confidence intervals for a meanAQA A-Level Further Maths: Mind map

Exam questions on Confidence intervals for a mean

1. The masses of packets of porridge oats are normally distributed with standard deviation $12$ g. A random sample of $36$ packets has mean mass $504$ g.
   Find a $99\%$ confidence interval for the population mean mass.2 marks
2. The time taken by a train to complete a journey is normally distributed with variance $9$ minutes$^2$. A random sample of $16$ journeys has mean time $42.5$ minutes.
   The rail company claims that the mean journey time is $45$ minutes. Use your interval from (b) to comment on this claim.2 marks
3. The lengths of trout on a fish farm are normally distributed with standard deviation $2.4$ cm. A random sample of $64$ trout has mean length $31.2$ cm.
   Construct a $95\%$ confidence interval for the mean length of trout on the farm.3 marks