| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Direct binomial from normal probability |
| Difficulty | Standard +0.3 This is a straightforward multi-part normal distribution question requiring standardization, inverse normal lookup, and binomial probability calculation. Part (i) is routine z-score calculation, part (ii) uses symmetry and tables, and part (iii) applies binomial distribution with the probability from part (i). All techniques are standard S1 material 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 probabilities2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
7 The weights, $X$ grams, of bars of soap are normally distributed with mean 125 grams and standard deviation 4.2 grams.\\
(i) Find the probability that a randomly chosen bar of soap weighs more than 128 grams.\\
(ii) Find the value of $k$ such that $\mathrm { P } ( k < X < 128 ) = 0.7465$.\\
(iii) Five bars of soap are chosen at random. Find the probability that more than two of the bars each weigh more than 128 grams.
\hfill \mbox{\textit{CAIE S1 2009 Q7 [11]}}