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H2 Math Summary Notes
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Pure Mathematics
Unit 1 Inequalities1 Question 
Unit 2 Graphing Techniques7 Questions

Unit 3 Transformation of Graphs2 Questions

Unit 4 Functions6 Questions

Unit 5 APGP & Recurrence Relations6 Questions

Unit 6 Sigma Notation6 Questions

Unit 7 Techniques of Differentiation2 Questions

Unit 8 Applications of Differentiation9 Questions

Unit 9 Maclaurin Series2 Questions

Unit 10 Techniques of Integration6 Questions

Unit 11 Applications of Integration4 Questions

Unit 12 Differential Equations2 Questions

Unit 13 Vectors11 Questions

Unit 14 Complex Numbers6 Questions

StatisticsUnit 15 Permutation and Combinations7 Questions

Unit 16 Probability5 Questions

Unit 17 Discrete Random Variable4 Questions

Unit 18 Binomial Distribution5 Questions

Unit 19 Normal Distribution7 Questions

Unit 20 Sampling and Estimation8 Questions

Unit 21 Hypothesis Testing6 Questions

Unit 22 Correlation and Linear Regression5 Questions
Lesson 21,
Question 3
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Worked Example 3
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A beverage company produces thousands of cans of soda each day. The volume of a soda in a can follows a normal distribution with mean \(355\) ml and standard deviation \(1.2\) ml.
Following the maintenance of the filling machine, there may have been a slight adjustment. To determine if the machine still produces \(355\) ml of soda per can, \(15\) randomly chosen cans are chosen. The volume, \(x\) ml, of the \(15\) cans of soda is summarised by
\(\sum{x}=5314.5\), \(\sum{{{x}^{2}}=1892040.25}\)
Assuming that the variance of the distribution is unaltered by the adjustment, test at the \(6\%\) significance level whether there is any change in the mean volume of the sod
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