# S1 May 13 model answers :)

On the box plot 24 was marked it was supposed to be 14 :D

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Sl MAY t3
1. A meteorologist believes that there is a relationship between the height above sea level,
ft m, and the air temperature, t
oC. Data is collected at the same time from 9 diflerent
places on the same mountain. The data is summarised in the table below.
h t400 1 100 260 840 900 550 1230 100 770
t 3 10 20 9 10 l3 5 24 16
:
[You may assume that Zh:7150, ) r:t to, >h'z :7171s00, >)P 1116'
:
>th - 64980 and S,, 371.561
(a) Calculate S,,, and S,,,,. Give your answers to 3 significant figures'
(3)
(b) Calculate the product moment corelation coefficient ior this data.
(2)
(c) State whether of not your value supports the use of a regression equation to predict the
air temperature at different heights on this mountain. Give a reason for your answer.
(1)
(d) Find the equation of the regression line ol I on ft giving your answer in the form
7: o+ bh.
(4)
(e) Interpret the value of b.
(1)
(f) Estimate the difference in air temperature between a height of 500 m and a height of
1000 m.
. (2)
o)
=- -O'q 52*
c) e\es/ r rS chse -16
-SuJ)est co-3tt"'e-
d) b. StX
= -o.ol5oa+
Strtr

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### Page 2

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I
oc. Yt
- O 'OrS
{x ea",'-. t^.*i:J, t^o.6"^ 1rl*, ttn - *c"^e
4+rrts bJ 6.ot5 .
-1 .S" c a\rf{err.. u- .…read more

### Page 3

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The marks of a group of female students in a statistics test are summarised in Figure I
Females
Males
10 20 30 40 50 60 '70 80 90 100
Mark
Figure 1
(a) Write down the mark which is exceeded by 7 5o/o of the female students'
(1)
The marks of a group of male students in the same statistics test are summarised by the
stem and leaf diagram below.…read more

### Page 4

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In the space provided on Figure 1 draw a box plot to represent the marks ofthe male
students, indicating clearly any outliers.
(s)
(d) Compare and contrast the marks of the male and the female students.
(2)
q,) z5
b) A=31 Qr tn + 8h, +(.
= 1--15
Q, |-^ = r5.5 tlbh= 5l
tnacLrcrr1 = 5\, I@.A = ln-
c> l.,^*r t.r.,..t. . +6 - t.Sx\a - 20'5 -,lt rs 6(,1
Orrtt.gf
v?W lrr.ttt = 63+l:Sxlt = 88.…read more

### Page 5

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In a company the 200 employees are classified as full{ime workers, part-time workers or
contractors.
The table below shows the number of employees in each category and whether they walk
to work or use some form oltransporl.
Walk Transpolt +.rt.r,L
Full{ime worker 2 8 l()
Part-time worker 35 15 lro
Contractor 30 50 go
+-+-& 6+ 133 ILOL)
The events F, H and C are that an employee is a full-time worker, part-time worker or

### Page 6

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The following table summarises the tifires, I minutes to the nearest minute, recorded for a
group of students to complete an exam.
ls-s e3 33 +o-s s3
Time (minutes) r ll 20 21 25 26-30 3l - 35 36 45 46-60
Number of students f, 6l 88 16 l3 1l l0
I
atn..

### Page 7

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E t' ,.t., g::O.S = 3A
t=r s At
62- l{tr2 I so
-'. @z- -- Lz.+ (3te)
- to.s
c-) -F_ o,
r,,,,, j
Zo.s
ol-ro-5= 5Q_
o So Lz lO 62-
:) o, =
ftxrc +lo's
9&-
tA'6 Csr)
,
I
A)
r 'r1.5
-t-
(Ds
r
2S'S :ft' ',
t
Gs = 2S'S
lso
lO-Z = tS.S-t8'6 = 6'9\ (:sp)
e) dc.{z\ rs haaur\3 post
+) or- , olrr arL. \cA effi
nA-c.c^n, rwc-.I. r^ro u}l cul.l
orlso nCJ.fCl- b.,f \$, rr.^.…read more

### Page 8

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A biased die with six faces is rolled. The discrete random variable x represents the score
on the uppermost face. The probability distribution of Xis shown in the table be1ow.
.x I 2 3 4 5 6
P(X: x) o a a b h 0.3
(a) Given that E(-l') :4.2 find the value of a and the value of D'
(s)
(b) Show that E(X2) -- 20.4
(1)
(c) Find Var(5 - 3,1)
(3)
A biased die with five faces is rollcd.…read more

### Page 9

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VCx) = 6(xz) -E(r)' = 20,t|-.+.2_z = L.+L
d) 5L= I r. [-=O.L
e>
r

### Page 10

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The weight, in grams, of beans in a tin is normally distributed with mean p and standard
deviation 7.8
Given that 10% of tins contain less than 200 g, find
(a) the value ofp
(3)
(b) the percentage oftins that contain more than 225 g ofbeans.
(3)
The machine settings are adjusted so that the weight, in grams, of beans in a tin is normally
distributed with mean 205 and standard deviation o.…read more