| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Independent probability calculations |
| Difficulty | Standard +0.3 This is a straightforward S1 normal distribution question requiring standard z-score calculations and independent probability multiplication. Part (d) adds slight conceptual depth by asking for comparison reasoning about combined distributions, but overall this is a routine textbook exercise with no novel problem-solving required. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks |
|---|---|
| (a) \(P(Z > \frac{165-156}{\sqrt{73}}) = P(Z > 1.05) = 0.1469\) | M2 A1 |
| (b) \(1 - (0.5 + 0.1469) = 0.3531\) | M1 A1 |
| (c) \(P(14yo > 165) = P(Z > \frac{165-160}{\sqrt{79}}) = P(Z > 0.56) = 0.2877\); \(P(\text{both} > 165) = 0.1469 \times 0.2877 = 0.0423\) (3sf) | M2 A1 M1 A1 |
| (d) more as e.g. answer to (c) satisfies condition but can also have one less than 165 if the other is sufficiently over 165 | B2 |
| (12) |
**(a)** $P(Z > \frac{165-156}{\sqrt{73}}) = P(Z > 1.05) = 0.1469$ | M2 A1 |
**(b)** $1 - (0.5 + 0.1469) = 0.3531$ | M1 A1 |
**(c)** $P(14yo > 165) = P(Z > \frac{165-160}{\sqrt{79}}) = P(Z > 0.56) = 0.2877$; $P(\text{both} > 165) = 0.1469 \times 0.2877 = 0.0423$ (3sf) | M2 A1 M1 A1 |
**(d)** more as e.g. answer to (c) satisfies condition but can also have one less than 165 if the other is sufficiently over 165 | B2 |
| | | (12) |
---3. A study was made of the heights of boys of different ages in Lancashire.
The study concluded that the heights of 13 year-old boys are normally distributed with a mean of 156 cm and a variance of $73 \mathrm {~cm} ^ { 2 }$.
Find the probability that a 13 year-old boy chosen at random will be
\begin{enumerate}[label=(\alph*)]
\item more than 165 cm tall,
\item between 156 and 165 cm tall.
The study also concluded that the heights of 14 year-old boys are normally distributed with a mean of 160 cm and a variance of $79 \mathrm {~cm} ^ { 2 }$.
One 13 year-old and one 14 year-old boy are chosen at random.
\item Find the probability that both boys are more than 165 cm tall.
\item State, with a reason, whether the probability that the combined height of the two boys is more than 330 cm is more or less than your answer to part (c).\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [12]}}