Mathematical Methods — Question 12

QCAA 2022, Paper 1 · 3 marks

Q12 · 2022 · Technology-freeSimple familiar3 marks

QUESTION 12 (3 marks)

The probability that a debating team wins a debate can be modelled as a Bernoulli distribution. Given that the probability of winning a debate is

\frac45

Determine the mean of this distribution.

[1 mark]

Determine the variance of this distribution.

[1 mark]

Determine the standard deviation of this distribution.

[1 mark]

WORKED SOLUTION

3 marks

ANSWER

\frac45

; b)

\frac4{25}

; c)

\frac25

Worked solution

E(X)=\sum p_i x_i=\frac15(0)+\frac45(1)=\frac45.

\operatorname{Var}(X)=\sum p_i(x_i-\mu)^2=\frac4{25}.

\text{Standard deviation}=\sqrt{\operatorname{Var}(X)}=\frac25.

correctly determines the mean

[1 mark]

correctly determines the variance

[1 mark]

determines the standard deviation

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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