| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Statistics (SPS ASFM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 8 |
| Topic | Geometric Distribution |
| Type | Geometric then binomial separate scenarios |
| Difficulty | Moderate -0.3 This is a straightforward geometric distribution question requiring standard formulas. Part (a) uses the mean formula E(X)=1/p, part (b) requires summing geometric probabilities or using the CDF, and part (c) involves recognizing a binomial distribution derived from the geometric. All parts are routine applications of textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
Every time a spinner is spun, the probability that it shows the number 4 is 0.2, independently of all other spins.
\begin{enumerate}[label=(\alph*)]
\item A pupil spins the spinner repeatedly until it shows the number 4.
Find the mean of the number of spins required. [2]
\item Calculate the probability that the number of spins required is between 3 and 10 inclusive. [2]
\item Each pupil in a class of 30 spins the spinner until it shows the number 4. Out of the 30 pupils, the number of pupils who require at least 10 spins is denoted by $X$.
Determine the variance of $X$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM Statistics 2021 Q4 [8]}}