The Binomial Distribution and Sampling Distribution of the Mean

We estimate ME12-BS is worth about 6 marks out of 100 under the new Mathematics Extension 1 syllabus. Practise 17 exam-style questions (multi-part, multiple choice, numerical answer) with instant marking and a worked solution for every question.

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Example questions

Example 1 · 1 mark · multiple choice

A Bernoulli random variable $X$ has $P (X = 1) = 0.2$ . What are $E (X)$ and $Var (X)$ ?

A $E (X) = 0.2$ , $Var (X) = 0.16$
B $E (X) = 0.2$ , $Var (X) = 0.04$
C $E (X) = 0.8$ , $Var (X) = 0.16$
D $E (X) = 0.5$ , $Var (X) = 0.25$

Example 2 · 4 marks · multi-part

30% of students at a school walk to school. A random sample of 10 students is chosen. Let $X$ be the number who walk.

Example 3 · 1 mark · multiple choice

A fair coin is tossed 8 times. What is the probability of getting at most 2 heads, correct to four decimal places?

A0.1445
B0.1094
C0.8555
D0.0352

Answers and worked solutions appear when you practise these questions.

The Binomial Distribution and Sampling Distribution of the Mean

Example questions

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