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Date November Example question Marks available 2 Reference code EXN.2.SL.TZ0.4
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Write down Question number 4 Adapted from N/A

Question

A dice manufacturer claims that for a novelty die he produces the probability of scoring the numbers 1 to 5 are all equal, and the probability of a 6 is two times the probability of scoring any of the other numbers.

To test the manufacture’s claim one of the novelty dice is rolled 350 times and the numbers scored on the die are shown in the table below.

A χ2 goodness of fit test is to be used with a 5% significance level.

Find the probability of scoring a six when rolling the novelty die.

[3]
a.

Find the probability of scoring more than 2 sixes when this die is rolled 5 times.

[4]
b.

Find the expected frequency for each of the numbers if the manufacturer’s claim is true.

[2]
c.i.

Write down the null and alternative hypotheses.

[2]
c.ii.

State the degrees of freedom for the test.

[1]
c.iii.

Determine the conclusion of the test, clearly justifying your answer.

[4]
c.iv.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

Let the probability of scoring 1,,5 be p,

5p+2p=1p=17        (M1)(A1)

Probability of 6=27         A1

 

[3 marks]

a.

Let the number of sixes be X

X~B5,27        (M1)

PX>2=PX3 or PX>2=1-PX2        (M1)

                 =0.145 0.144701        (M1)A1

 

[4 marks]

b.

Expected frequency is 350×p or 350×2p        (M1)

         A1

 

[2 marks]

c.i.

H0: The manufacture’s claim is correct         A1
H1: The manufacturer’s claim is not correct         A1

 

[2 marks]

c.ii.

Degrees of freedom =5       A1

 

[1 mark]

c.iii.

p-value =0.0984 0.0984037       (M1)A1

0.0984>0.05          R1

Hence insufficient evidence to reject the manufacture’s claim.       A1

 

[4 marks]

c.iv.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
c.iii.
[N/A]
c.iv.

Syllabus sections

Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
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Topic 4—Statistics and probability

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