| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | November |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Find p then binomial probability |
| Difficulty | Standard +0.3 This is a standard multi-part normal distribution question requiring inverse normal calculation to find σ, then straightforward probability calculations and binomial applications. All techniques are routine for S1 level 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 probabilities2.04d Normal approximation to binomial2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
7 The times spent by people visiting a certain dentist are independent and normally distributed with a mean of 8.2 minutes. $79 \%$ of people who visit this dentist have visits lasting less than 10 minutes.\\
\begin{enumerate}[label=(\roman*)]
\item Find the standard deviation of the times spent by people visiting this dentist.
\item Find the probability that the time spent visiting this dentist by a randomly chosen person deviates from the mean by more than 1 minute.
\item Find the probability that, of 6 randomly chosen people, more than 2 have visits lasting longer than 10 minutes.
\item Find the probability that, of 35 randomly chosen people, fewer than 16 have visits lasting less than 8.2 minutes.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2010 Q7 [14]}}