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

Exam questions on Confidence intervals for a Normal mean

1. The masses of bags of flour are Normally distributed with a known standard deviation of $8$ g. A random sample of $25$ bags has a mean mass of $1012$ g.
   Find a $90\%$ confidence interval for the mean mass of a bag.2 marks
2. A $95\%$ confidence interval for the mean $\mu$ of a Normal population with known standard deviation $10$ is $(49.2,\ 54.8)$. It was calculated from a random sample.
   Use the confidence interval to carry out a test of $H_0:\mu=50$ against $H_1:\mu\neq50$ at the $5\%$ significance level, stating your conclusion.2 marks
3. The time taken, in minutes, for a train journey is Normally distributed with a known standard deviation of $4.5$ minutes. A random sample of $36$ journeys has a mean time of $52.4$ minutes.
   Find a $99\%$ confidence interval for the mean journey time.3 marks