| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 11 |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Standard +0.3 This is a straightforward Further Maths statistics question involving standard normal distribution techniques: finding percentiles using inverse normal, binomial probability with normal probabilities, and working backwards from a percentile to find standard deviation. All parts are routine applications of well-practiced methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04c Calculate binomial probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
The random variable $X$ represents the weight in kg of a randomly selected male dog of a particular breed. $X$ is Normally distributed with mean 30.7 and standard deviation 3.5.
\begin{enumerate}[label=\roman*)]
\item Find the 90th percentile for the weights of these dogs. [2]
\item Five of these dogs are chosen at random. Find the probability that exactly four of them weighs at least 30 kg. [3]
\end{enumerate}
The weights of females of the same breed of dog are Normally distributed with mean 26.8 kg.
\begin{enumerate}[label=\roman*)]
\setcounter{enumi}{2}
\item Given that 5% of female dogs of this breed weigh more than 30 kg, find the standard deviation of their weights. [3]
\item Sketch the distributions of the weights of male and female dogs of this breed on a single diagram. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2025 Q6 [11]}}