| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Topic | Normal Distribution |
| Type | Find p then binomial probability |
| Difficulty | Standard +0.3 This is a standard normal distribution problem requiring inverse normal calculations to find parameters from given probabilities, followed by a straightforward binomial probability calculation. While it involves multiple steps and two different distributions, the techniques are routine for Further Maths students with no novel problem-solving required. |
| Spec | 2.04c Calculate binomial probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
The weights of sacks of potatoes are normally distributed. It is known that one in five sacks weigh more than 6kg and three in five sacks weigh more than 5.5kg.
\begin{enumerate}[label=(\roman*)]
\item Find the mean and standard deviation of the weights of potato sacks. [5]
\item The sacks are put into crates, with twelve sacks going into each crate. What is the probability that a given crate contains two or more sacks that weigh more than 6kg?
You must explain your reasoning clearly in this question. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q4 [9]}}