| 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.\\
(i) Find the standard deviation of the times spent by people visiting this dentist.\\
(ii) Find the probability that the time spent visiting this dentist by a randomly chosen person deviates from the mean by more than 1 minute.\\
(iii) Find the probability that, of 6 randomly chosen people, more than 2 have visits lasting longer than 10 minutes.\\
(iv) Find the probability that, of 35 randomly chosen people, fewer than 16 have visits lasting less than 8.2 minutes.
\hfill \mbox{\textit{CAIE S1 2010 Q7 [14]}}