Question 1 - A-Level Maths

CAIE S2 2012 November — Question 1 3 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2012
Session	November
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Linear combinations of normal random variables
Type	Sum or total of normal variables
Difficulty	Moderate -0.5 This is a straightforward application of the standard result that the sum of independent normal variables is normal, requiring only recall of the formulas for mean (8×3.5) and variance (8×0.12²) of the sum. It's slightly easier than average as it's a direct one-step application with no problem-solving or interpretation required.
Spec	5.04b Linear combinations: of normal distributions

1 The lengths of logs are normally distributed with mean 3.5 m and standard deviation 0.12 m . Describe fully the distribution of the total length of 8 randomly chosen logs.

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Question 1:

Answer	Marks	Guidance
Answer/Working	Mark	Guidance
Normal with mean 28	B1	Both
\(\text{Var} = 0.12^2 \times 8 = 0.115\) (3 sfs)	M1	Square \(\sigma \times\) by 8 or \(\text{sd} = 0.12 \times \sqrt{8}\)
A1 [3]	or \(\text{sd} = 0.339\) (3 sfs); clearly state var/sd

## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Normal with mean 28 | B1 | Both |
| $\text{Var} = 0.12^2 \times 8 = 0.115$ (3 sfs) | M1 | Square $\sigma \times$ by 8 or $\text{sd} = 0.12 \times \sqrt{8}$ |
| | A1 [3] | or $\text{sd} = 0.339$ (3 sfs); clearly state var/sd |

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1 The lengths of logs are normally distributed with mean 3.5 m and standard deviation 0.12 m . Describe fully the distribution of the total length of 8 randomly chosen logs.

\hfill \mbox{\textit{CAIE S2 2012 Q1 [3]}}

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