May/June 2026 Paper 61

2026 · 6 questions · 17 parts · 50 marks

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Context for question 4

The score on one spin of a 5-sided spinner is denoted by the random variable

X

with probability distribution as shown in the table.

$x$	1	2	3	4	5
$P (X = x)$	0.1	0.3	0.4	0.1	0.1

4(a)Discrete Random VariablesEasy1 mark

Show that

E (X) = 2.8

Show your working

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4(b)Sampling Distributions Central Limit TheoremHard4 marks

It is given that

Var (X) = 1.16

The spinner is spun 300 times. The score on each spin is noted and the mean,

\overline{X}

, of the 300 scores is found.

Given that

P (2.8 - k < \overline{X} < 2.8 + k) = 0.2

, find the value of

k

Show your working

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k

4(c)Sampling Distributions Central Limit TheoremEasy1 mark

Explain why it was necessary to use the Central Limit Theorem in your answer to 4(b).

Answer

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4(d)Hypothesis TestingHard5 marks

For another similar spinner, it is claimed that

E (X) = 2.8

. Fred suspects that this value is incorrect. The spinner is spun 300 times, and the mean of the 300 scores is found to be

2.92

Given that the variance of the score on one spin of this spinner is also

1.16

, test Fred's suspicion at the

5%

significance level.

Show your working and conclusion

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