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

Exam questions on Confidence intervals for a Normal mean

1. The mass of a packet of flour, in grams, is Normally distributed with standard deviation $6$. A random sample of $25$ packets has mean mass $503.2$ g.
   The label says the mean mass is $500$ g. Use your interval from part (b) to comment on this claim, explaining the link with a hypothesis test.2 marks
2. A random sample of $36$ observations is taken from a Normal distribution with standard deviation $2.4$. The sample mean is $13.0$.
   The sample size is to be increased so that the width of the $90\%$ confidence interval is at most $0.8$. Find the smallest sample size required.2 marks
3. The time of one machine cycle, in seconds, is Normally distributed with standard deviation $0.5$. The mean of a random sample of $40$ cycles is $12.84$ s.
   Calculate a $99\%$ confidence interval for the mean cycle time.3 marks