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Date November 2020 Marks available 1 Reference code 20N.1.SL.TZ0.S_8
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number S_8 Adapted from N/A

Question

Each athlete on a running team recorded the distance (M miles) they ran in 30 minutes.

The median distance is 4 miles and the interquartile range is 1.1 miles.

This information is shown in the following box-and-whisker plot.

The distance in miles, M, can be converted to the distance in kilometres, K, using the formula K=85M.

The variance of the distances run by the athletes is 169km2.

The standard deviation of the distances is b miles.

A total of 600 athletes from different teams compete in a 5km race. The times the 600 athletes took to run the 5km race are shown in the following cumulative frequency graph.

There were 400 athletes who took between 22 and m minutes to complete the 5km race.

Find the value of a.

[2]
a.

Write down the value of the median distance in kilometres (km).

[1]
b.

Find the value of b.

[4]
c.

Find m.

[3]
d.

The first 150 athletes that completed the race won a prize.

Given that an athlete took between 22 and m minutes to complete the 5km race, calculate the probability that they won a prize.

[5]
e.

Markscheme

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

valid approach     (M1)

eg    Q3-Q1 , Q3-1.1 , 4.5-a=1.1

a=3.4      A1   N2

[2 marks]

a.

325 =6.4 (km)       A1   N1

[1 mark]

b.

METHOD 1 (standard deviation first)

valid approach        (M1)

eg    standard deviation=variance , 169

standard deviation=43 (km)       (A1)

valid approach to convert their standard deviation        (M1)

eg     43×58 , 169=85M

2024 (miles)  =56      A1   N3

 

Note: If no working shown, award M1A1M0A0 for the value 43.
If working shown, and candidate’s final answer is 43, award M1A1M0A0.

 

METHOD 2 (variance first)

valid approach to convert variance        (M1)

eg   582 , 6425 , 169×582

variance =2536       (A1)

valid approach        (M1)

eg    standard deviation=variance , 2536 , 169×582

2024 (miles)  =56      A1   N3

[4 marks]

c.

correct frequency for 22 minutes       (A1)

eg    20

adding their frequency (do not accept 22+400)       (M1)

eg    20+400 , 420 athletes

m=30 (minutes)         A1   N3

[3 marks]

d.

27 (minutes)       (A1)

correct working      (A1)

eg    130 athletes between 22 and 27 minutes, P22<t<27=150-20600 , 1360

evidence of conditional probability or reduced sample space      (M1)

eg    PAB , Pt<2722<t<30 , P22<t<27P22<t<m , 150400

correct working      (A1)

eg    130600400600 , 150-20400

130400 1340=78000240000=3901200=0.325      A1     N5

 

Note: If no other working is shown, award A0A0M1A0A0 for answer of 150400.
Award N0 for answer of 38 with no other working shown.

 

[5 marks]

e.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
Show 109 related questions
Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
Topic 4—Statistics and probability » SL 4.5—Probability concepts, expected numbers
Topic 4—Statistics and probability

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