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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…

Page 2

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)f.x )=z+ri

o) ,-r.
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- .

Page 3

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2. 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…

Page 4

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(c) 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,…

Page 5

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3. 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…

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…

Page 7

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ro.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…

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…

Page 9

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c) VCx) = 6(xz) -E(r)' = 20,t|-.+.2_z = L.+L



d) 5L= I r. [-=O.L
e>
r
T) P(s,..,. -2-) - P(x=\)J,\)' o,t * ia - l-
t(D

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…

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