Choosing and critiquing statistical modelsAQA A-Level Maths: Mind map

Exam questions on Choosing and critiquing statistical models

1. A teacher models the number $X$ of pupils in a class of $30$ who walk to school by the binomial distribution $X\sim B(30,0.4)$.
   The pupils in the class live at very different distances from the school. Explain why $B(30,0.4)$ may not be a suitable model.2 marks
2. A researcher records the monthly household income $X$ pounds in a city. The sample mean is $2400$, the sample median is $1900$ and the sample standard deviation is $1800$. She models $X$ by the Normal distribution $N(2400,1800^2)$.
   State, with a reason, whether the Normal model is appropriate for monthly household income.2 marks
3. A call centre claims that $70\%$ of calls are answered within $20$ seconds. A manager records the next $10$ calls received on a Monday morning and models the number $X$ answered within $20$ seconds by $X\sim B(10,0.7)$.
   State the distribution of $X$ and find the probability that at least $8$ of the $10$ calls are answered within $20$ seconds.3 marks