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Date November 2017 Marks available 3 Reference code 17N.2.SL.TZ0.S_8
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number S_8 Adapted from N/A

Question

Adam is a beekeeper who collected data about monthly honey production in his bee hives. The data for six of his hives is shown in the following table.

N17/5/MATME/SP2/ENG/TZ0/08

The relationship between the variables is modelled by the regression line with equation P = a N + b .

Adam has 200 hives in total. He collects data on the monthly honey production of all the hives. This data is shown in the following cumulative frequency graph.

N17/5/MATME/SP2/ENG/TZ0/08.c.d.e

Adam’s hives are labelled as low, regular or high production, as defined in the following table.

N17/5/MATME/SP2/ENG/TZ0/08.c.d.e_02

Adam knows that 128 of his hives have a regular production.

Write down the value of a and of b .

[3]
a.

Use this regression line to estimate the monthly honey production from a hive that has 270 bees.

[2]
b.

Write down the number of low production hives.

[1]
c.

Find the value of k ;

[3]
d.i.

Find the number of hives that have a high production.

[2]
d.ii.

Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.

[3]
e.

Markscheme

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

evidence of setup     (M1)

eg correct value for a or b

a = 6.96103 ,   b = 454.805

a = 6.96 ,   b = 455  (accept  6.96 x 455 )     A1A1     N3

[3 marks]

a.

substituting N = 270 into their equation     (M1)

eg 6.96 ( 270 ) 455

1424.67

P = 1420  (g)     A1     N2

[2 marks]

b.

40 (hives)     A1     N1

[1 mark]

c.

valid approach     (M1)

eg 128 + 40

168 hives have a production less than k     (A1)

k = 1640     A1     N3

[3 marks]

d.i.

valid approach     (M1)

eg 200 168

32 (hives)     A1     N2

[2 marks]

d.ii.

recognize binomial distribution (seen anywhere)     (M1)

eg X B ( n ,   p ) ,   ( n r ) p r ( 1 p ) n r

correct values     (A1)

eg n = 40 (check FT) and p = 0.75  and  r = 30 ,   ( 40 30 ) 0.75 30 ( 1 0.75 ) 10

0.144364

0.144     A1     N2

[3 marks]

e.

Examiners report

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

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 4.4—Pearsons, scatter diagrams, eqn of y on x
Topic 4—Statistics and probability » SL 4.8—Binomial distribution
Topic 4—Statistics and probability

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