| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2017 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Direct binomial from normal probability |
| Difficulty | Easy -1.2 This question tests basic recall of fundamental properties: (a) requires knowing that P(W=k)=0 for continuous distributions, (b) is a direct binomial probability calculation using the formula or calculator, and (c) requires calculating mean and SD for binomial then finding a probability. All parts are routine applications of standard formulas with no problem-solving or insight required. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
\begin{enumerate}
\item The continuous random variable $W$ has the normal distribution $\mathrm { N } \left( 32,4 { } ^ { 2 } \right)$\\
(a) Write down the value of $\mathrm { P } ( W = 36 )$
\end{enumerate}
The discrete random variable $X$ has the binomial distribution $\mathrm { B } ( 20,0.45 )$\\
(b) Find $\mathrm { P } ( X = 8 )$\\
(c) Find the probability that $X$ lies within one standard deviation of its mean.\\
\hfill \mbox{\textit{Edexcel S2 2017 Q1 [7]}}