N2021 P2 Q6

Junior College 2

7 marks

A biased $5$-sided spinner gives the scores $1$, $2$, $3$, $4$ and $5$ with the probabilities shown in the table, where $p$ and $q$ are constants.

Score	$1$	$2$	$3$	$4$	$5$
Probability	$0.2$	$0.3$	$p$	$p$	$q$

Given that the variance of the score is $1.61$, calculate the mean score.[7]

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Answer:Mean score $=2.7$.

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Score	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)
Probability	\(0.2\)	\(0.3\)	\(p\)	\(p\)	\(q\)