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Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ2.T_7
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 2
Command term Write down Question number T_7 Adapted from N/A

Question

A tetrahedral (four-sided) die has written on it the numbers 1, 2, 3 and 4. The die is rolled many times and the scores are noted. The table below shows the resulting frequency distribution.

M17/5/MATSD/SP1/ENG/TZ2/07

The die was rolled a total of 100 times.

The mean score is 2.71.

Write down an equation, in terms of x and y , for the total number of times the die was rolled.

[1]
a.

Using the mean score, write down a second equation in terms of x and y .

[2]
b.

Find the value of x and of y .

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

18 + x + y + 22 = 100 or equivalent     (A1)     (C1)

[1 mark]

a.

18 + 2 x + 3 y + 88 100 = 2.71 or equivalent     (M1)(A1)     (C2)

 

Note:     Award (M1) for a sum including x and y , divided by 100 and equated to 2.71, (A1) for a correct equation.

 

[2 marks]

b.

x + y = 60 and 2 x + 3 y = 165     (M1)

 

Note:     Award (M1) for obtaining a correct linear equation in one variable from their (a) and their (b).

This may be implied if seen in part (a) or part (b).

 

x = 15 ;   y = 45     (A1)(ft)(A1)(ft)     (C3)

 

Notes:     Follow through from parts (a) and (b), irrespective of working seen provided the answers are positive integers.

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
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Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
Topic 4—Statistics and probability

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