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Date May 2018 Marks available 1 Reference code 18M.1.SL.TZ2.T_12
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 2
Command term Write down Question number T_12 Adapted from N/A

Question

The histogram shows the time, t, in minutes, that it takes the customers of a restaurant to eat their lunch on one particular day. Each customer took less than 25 minutes.

The histogram is incomplete, and only shows data for 0 ≤ t < 20.

The mean time it took all customers to eat their lunch was estimated to be 12 minutes.

It was found that k customers took between 20 and 25 minutes to eat their lunch.

Write down the mid-interval value for 10 ≤ t < 15.

[1]
a.

Write down the total number of customers in terms of k.

[1]
b.i.

Calculate the value of k.

[3]
b.ii.

Hence, complete the histogram.

[1]
c.

Markscheme

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

12.5     (A1) (C1)

[1 mark]

a.

33 + k  OR  10 + 8 + 5 + 10 + k     (A1)

Note: Award (A1) for “number of customers = 33 + k”.

[1 mark]

b.i.

2.5 × 10 + 7.5 × 8 + + 22.5 × k 33 + k = 12      (M1)(A1)(ft)

Note: Award (M1) for substitution into the mean formula and equating to 12, (A1)(ft) for their correct substitutions.

(k =) 7     (A1)(ft) (C4)

Note: Follow through from part (b)(i) and their mid-interval values, consistent with part (a). Do not award final (A1) if answer is not an integer.

[3 marks]

b.ii.

(A1)(ft) (C1)

Note: Follow through from their part (b)(ii) but only if the value is between 1 and 10, inclusive.

[1 mark]

 

c.

Examiners report

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