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Date May 2017 Marks available 2 Reference code 17M.1.SL.TZ2.S_8
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number S_8 Adapted from N/A

Question

A city hired 160 employees to work at a festival. The following cumulative frequency curve shows the number of hours employees worked during the festival.

M17/5/MATME/SP1/ENG/TZ2/08.a.ii

The city paid each of the employees £8 per hour for the first 40 hours worked, and £10 per hour for each hour they worked after the first 40 hours.

Find the median number of hours worked by the employees.

[2]
a.i.

Write down the number of employees who worked 50 hours or less.

[1]
a.ii.

Find the amount of money an employee earned for working 40 hours;

[1]
b.i.

Find the amount of money an employee earned for working 43 hours.

[3]
b.ii.

Find the number of employees who earned £200 or less.

[3]
c.

Only 10 employees earned more than £ k . Find the value of k .

[4]
d.

Markscheme

evidence of median position     (M1)

eg 80th employee

40 hours     A1     N2

[2 marks]

a.i.

130 employees     A1     N1

[1 mark]

a.ii.

£320     A1     N1

[1 mark]

b.i.

splitting into 40 and 3     (M1)

eg 3 hours more, 3 × 10

correct working     (A1)

eg 320 + 3 × 10

£350     A1     N3

[3 marks]

b.ii.

valid approach     (M1)

eg 200 is less than 320 so 8 pounds/hour, 200 ÷ 8 ,   25 ,   200 320 = x 40 ,

18 employees     A2     N3

[3 marks]

c.

valid approach     (M1)

eg 160 10

60 hours worked     (A1)

correct working     (A1)

eg 40 ( 8 ) + 20 ( 10 ) ,   320 + 200

k = 520     A1     N3

[4 marks]

d.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.
[N/A]
d.

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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