Populations, censuses and samplesEdexcel International A Level Further Maths: Mind map

Exam questions on Populations, censuses and samples

1. A council keeps a register of the $4200$ households in its area. To find out how many households recycle, it selects $300$ households from the register and sends each one a questionnaire.
   Give one advantage and one disadvantage of the council using a sample of $300$ households rather than a census.2 marks
2. The masses of bags of flour are modelled by $\mathrm{N}(\mu,\sigma^2)$, where $\mu$ and $\sigma$ are unknown. A random sample $X_1,X_2,X_3,X_4,X_5$ of bags is taken and $\bar X$ is the sample mean.
   Explain why $\bar X$ has a sampling distribution but $\mu$ does not.2 marks
3. A bag contains three discs numbered $1$, $2$ and $3$. A disc is drawn at random and replaced, and then a second disc is drawn at random. Let $M$ be the larger of the two numbers drawn (or the common value if they are equal) and let $\bar X$ be the mean of the two numbers.
   Find the sampling distribution of $M$.3 marks