H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Unit 3 Transformation of Graphs
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Unit 4 Functions
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How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
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Unit 12 Differential Equations
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Unit 13 Vectors
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Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Worked Example 7

H2 Math Summary Notes Unit 19 Normal Distribution Worked Example 7

The heights, in metres, of female and male students in a school follow normal distributions with the following data.

Find the probability that

(i)

Two randomly selected male are taller than twice a randomly selected female.

(ii)

A randomly selected male student is taller than a randomly selected female student by at least [latex]20[/latex] cm.

(iii)

The difference in height between a randomly selected male and a female is more than [latex]30[/latex] cm.

(iv)

The heights of two randomly selected female students both exceed [latex]1.5[/latex] m.

(v)

The total height of two randomly selected female students is more than [latex]3[/latex] m.

Comment on the difference in answers for part (iv) and (v).

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